AnaJaved-L05-M02-HypothesisSim.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Milestone 2 - Hypothesis Simulation \n",
    "\n",
    "## Author - Ana Javed\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Instructions\n",
    "Use the <a href=\"https://archive.ics.uci.edu/ml/datasets/Automobile\">automotive data set</a> to perform the following:\n",
    "\n",
    "1. Identify a likely distribution for price and several other features.\n",
    "2. Compute basic summary statistics by both classical, bootstrap, and Bayesian methods\n",
    "3. Compute confidence intervals for these summary statistics by classical, bootstrap, and Bayesian methods\n",
    "4. Correctly use hypothesis tests to determine if the differences in pairs and multiple populations are significant:\n",
    "            Classical tests\n",
    "            Tukey’s Honest Significant Differences (HSD)\n",
    "            Bootstrap methods\n",
    "            Bayesian model\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note\n",
    "Please clearly outline the results with markdown text. Be sure your discussion includes narrative for your figures and tables so it is clear to the reader the importance of each bit of evidence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "fileName = \"https://library.startlearninglabs.uw.edu/DATASCI410/Datasets/Automobile%20price%20data%20_Raw_.csv\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import libraries & packages required \n",
    "import pandas as pd\n",
    "import numpy as np \n",
    "import scipy as scipy \n",
    "from scipy import stats\n",
    "import scipy.stats as ss\n",
    "import statsmodels.stats.weightstats as ws\n",
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from statistics import mean\n",
    "import numpy.random as nr\n",
    "from matplotlib import pyplot\n",
    "from statsmodels.stats.multicomp import pairwise_tukeyhsd \n",
    "\n",
    "# Declaring inline visualizations \n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Cleaned up Dataset location\n",
    "fileName = \"https://library.startlearninglabs.uw.edu/DATASCI410/Datasets/Automobile%20price%20data%20_Raw_.csv\"\n",
    "\n",
    "# Reading file into a Pandas Dataframe \n",
    "Auto = pd.read_csv(fileName)\n",
    "\n",
    "### Some Exploratory Data Analysis \n",
    "# print(Auto.describe()) # Summary Statistics\n",
    "\n",
    "# print(Auto.shape) # DF dimensions\n",
    "\n",
    "# Auto.head(5) # Top 5 rows\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.) Identify a likely distribution for price and several other features. \n",
    "For example, you should determine if the price is better represented by the log of price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### Creating New A few New Columns: Log Price, Log City-MPG, Log engine-size , and Log Length\n",
    "\n",
    "############ Log Price \n",
    "# Converting Unknown \"?\" Values in Price Column \n",
    "Auto.loc[:,'price'] = pd.to_numeric(Auto.loc[:,'price'], errors='coerce')    \n",
    "HasNan1 = np.isnan(Auto.loc[:,'price'])\n",
    "Auto.loc[HasNan1,'price'] = np.nanmedian(Auto.loc[:,'price'])\n",
    "\n",
    "# Creating New Log Price Column from Price Column\n",
    "Auto.loc[:, \"LogPrice\"] = np.log(Auto.loc[:, \"price\"])\n",
    "\n",
    "# Verifying Output looks correct\n",
    "# print(Auto.loc[:, \"price\"].value_counts()) \n",
    "# print(Auto.loc[:, \"LogPrice\"].value_counts()) \n",
    "\n",
    "############ Log City-MPG \n",
    "# Converting Unknown \"?\" Values in city-mpg Column \n",
    "Auto.loc[:,'city-mpg'] = pd.to_numeric(Auto.loc[:,'city-mpg'], errors='coerce')    \n",
    "HasNan1 = np.isnan(Auto.loc[:,'city-mpg'])\n",
    "Auto.loc[HasNan1,'city-mpg'] = np.nanmedian(Auto.loc[:,'city-mpg'])\n",
    "\n",
    "## Creating New Log city-mpg Column from city-mpg Column\n",
    "Auto.loc[:, \"log-city-mpg\"] = np.log(Auto.loc[:, \"city-mpg\"])\n",
    "\n",
    "\n",
    "############ Log Engine Size \n",
    "# Converting Unknown \"?\" Values in engine-size  Column \n",
    "Auto.loc[:,'engine-size'] = pd.to_numeric(Auto.loc[:,'engine-size'], errors='coerce')    \n",
    "HasNan1 = np.isnan(Auto.loc[:,'engine-size'])\n",
    "Auto.loc[HasNan1,'engine-size'] = np.nanmedian(Auto.loc[:,'engine-size'])\n",
    "\n",
    "## Creating New Log engine-size Column from engine-size Column\n",
    "Auto.loc[:, \"log-engine-size\"] = np.log(Auto.loc[:, \"engine-size\"])\n",
    "\n",
    "\n",
    "############ Log Engine Size \n",
    "# Converting Unknown \"?\" Values in length Column \n",
    "Auto.loc[:,'length'] = pd.to_numeric(Auto.loc[:,'length'], errors='coerce')    \n",
    "HasNan1 = np.isnan(Auto.loc[:,'length'])\n",
    "Auto.loc[HasNan1,'length'] = np.nanmedian(Auto.loc[:,'length'])\n",
    "\n",
    "## Creating New Log length Column from length Column\n",
    "Auto.loc[:, \"loglength\"] = np.log(Auto.loc[:, \"length\"])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Creating a Q-Q Plot for a Normal Distribution\n",
    "\n",
    "## Function to Create Q-Q Plot \n",
    "def qq_plot(vec1, vec2, title_name, color = \"blue\"):\n",
    "    import matplotlib.pyplot as plt\n",
    "    import scipy.stats as ss\n",
    "    \n",
    "    plt.figure(figsize=(10, 8)).gca() # define axis\n",
    "    \n",
    "    ax1 = plt.subplot(221) ## setup the left subplot\n",
    "    ss.probplot(vec1, plot = ax1, dist ='norm') ## Plot the left subplot\n",
    "    ax1.set_title(\"Probplot for {0} Column\".format(title_name))\n",
    "    ax1.get_lines()[0].set_markerfacecolor(color)\n",
    "    \n",
    "    ax1 = plt.subplot(222) ## Set up the right subplot\n",
    "    ss.probplot(vec2, plot = ax1, dist = 'norm') ## Plot the right subplot\n",
    "    ax1.set_title(\"Probplot for {0} Log Column\".format(title_name))\n",
    "    ax1.get_lines()[0].set_markerfacecolor(color)\n",
    "    \n",
    "# Passing Price and LogPrice Columns to the Q-Q Plot Function\n",
    "qq_plot(Auto.loc[:, 'price'], Auto.loc[:, 'LogPrice'], \"Price\", 'blue')    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With these q-q plots for price, we visually see a greater distance at the top and bottom for Price column. The LogPrice column also has this curvature, but it is not as large. Price Log has a better fit to the line. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Passing City MPG and Log City MPG Columns to the Q-Q Plot Function\n",
    "qq_plot(Auto.loc[:, 'city-mpg'], Auto.loc[:, 'log-city-mpg'], \"City MPG\", \"red\")    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With these q-q plots for city-mpg, we visually see a greater distance at the top and bottom for the city-mpg column. The Log City MPG column also has this pattern, but it is not as large and it is closer to the line. Log City MPG is a better fit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Passing Engine Size and Log Engine Size Columns to the Q-Q Plot Function\n",
    "qq_plot(Auto.loc[:, 'engine-size'], Auto.loc[:, 'log-engine-size'], \"Engine Size\", \"white\")    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With these q-q plots for engine size, we visually see a greater distance at the top and bottom for the engine size column. The Log engine size column also has this pattern, but the distance is minimal, and it too is closer to the line. Log Engine Size is a better fit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Passing length and Log length Columns to the Q-Q Plot Function\n",
    "qq_plot(Auto.loc[:, 'length'], Auto.loc[:, 'loglength'], \"Length\", \"cyan\")    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With these q-q plots for length, we visually see a slightly bigger distance at the top and bottom for the Log length column. The regular length column is closer to the normal distribution line and is a better fit than the log length column. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.) Compute basic summary statistic of the mean by both classical bootstrap and Bayesian methods "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I will move forward with the assignment using one column, specifically the LogPrice Column since it was a better fit to the normal distribution than the Price column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    205.000000\n",
       "mean       9.347955\n",
       "std        0.497540\n",
       "min        8.540519\n",
       "25%        8.960339\n",
       "50%        9.239414\n",
       "75%        9.711116\n",
       "max       10.723267\n",
       "Name: LogPrice, dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Gathering Sample Statistics for LogPrice\n",
    "Auto.loc[:, \"LogPrice\"].describe()\n",
    "\n",
    "# mean  =     9.347955\n",
    "# std   =     0.497540"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='LogPrice', ylabel='Density'>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Creating a density plot of LogPrice to visualize the distribution prior to bootstrapping\n",
    "sns.kdeplot(Auto.loc[:, \"LogPrice\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Bootstrapping LogPrice over 10,000 samples: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Function to Plot a Histogram + Confidence Intervals \n",
    "def plot_hist(x, p=5):\n",
    "    # Plot the distribution and mark the mean\n",
    "    pyplot.hist(x, alpha=.5)\n",
    "    pyplot.axvline(x.mean())\n",
    "    # 95% confidence interval    \n",
    "    pyplot.axvline(np.percentile(x, p/2.), color='red', linewidth=3)\n",
    "    pyplot.axvline(np.percentile(x, 100-p/2.), color='red', linewidth=3)\n",
    "    \n",
    "    print(\"Confidence Interval Range: \", \n",
    "          np.percentile(x, p/2.),\" to \" , \n",
    "          np.percentile(x, 100-p/2.))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence Interval Range:  9.28100323171516  to  9.415390558974442\n",
      "--------------------------\n",
      "Bootstrapping Price Mean: \n",
      "9.347993669006504\n",
      "\n",
      "\n",
      "LogPrice Sample Mean: \n",
      "9.347954638082927\n",
      "--------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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H7ANIMlNV06vdsUlznBuL49xYNtI41/pC7iywdej5FuD4GvdBkrq11qH/D8C2JFcl+XZgN3BwjfsgSd1a0+mdqjqV5KPAXwCbgE9W1dFFdtu3+j07LzjOjcVxbiwbZpxreiFXkjRZfiJXkjpi6EtSRyYa+kk+luTJJEeTfHzE9p9N8sW2fDbJ24e2rZuvc1jmOF9MciTJE0lm1rTj52iMce5qY3wiyUySHx3atpGO50Lj3DDHc6jdDyU53T6Hc6a2YY7nULtR41w3x/ObqmoiC6996Oo7GVxQ/itg27w2PwJc0tZ/Cvh8W98E/BPwvcC3A/8IbJ/UWFZrnO35i8Clkx7HCo3zTbx2HekHgGc26PEcOc6NdjyHjt1fA58GPrARj+fZxrmejufwMskz/e8HPldV/1ZVp4C/A94/3KCqPltVX29PP8fgvn4Y+jqHqvoP4MzXOZyPljPO9WSccX6j2k8K8EZe+2DeRjueZxvnerLoOJtfBD4FnByqbajj2Ywa57o0ydB/EnhXkrcm+U7gfXzrB7fmuxV4pK1vBl4a2jbbauej5YwTBoHxl0kOt6+nOF+NNc4k70/yDPBnwM+18oY7nmcZJ2yg45lkM4OA/L15+26o47nAOGH9HM9vmthfzqqqp5P8H+AQ8A0G/wU8Naptkh9jEIZn5kbH+jqH88Eyxwnwzqo6nuQy4FCSZ6rqM6vd73M17jir6iHgoSTvAv438BNswON5lnHCxjqevwP8r6o6nXzLIdxox/N3GD1OWCfHc9hEL+RW1Seq6ger6l3A14Dn57dJ8gPA/wN2VdVXW3ldfZ3DMsZJVR1vjyeBhxj81/m8NM44h9p+BnhbkkvZgMdzqO3wODfa8ZwGHkzyIvAB4N4kN7HxjufZxrmujuc3TfKCAnBZe/xu4Bnaxcyh7d8NHAN+ZF79AuBLwFW8dqHomkmOZZXG+UbgzUPrn2XwLaUTH9MSx/l9vHaB8weBrzA4K9xox/Ns49xQx3Ne2/t57ULuhjqeC4xzXR3PM8uk/zD6p5K8FfhP4Paq+nqSXwCoqt8DfgV4K4PfrACnqmq6lvZ1DpO0pHEClzOYIoDBD9IfVtWfT2IAY1psnD8N3JzkP4F/B36mBj8xG+14jhxnko12PEfagD+fZ7Pejifg1zBIUlf8RK4kdcTQl6SOGPqS1BFDX5I6YuhLUkcMfUnqiKEvSR35b/eyTNssWUBNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Bootstrapping the LogPrice Mean\n",
    "n = 10000  # going to conduct 10,000 realizations \n",
    "\n",
    "LogPrice_bootstrap_means = pd.Series([\n",
    "    Auto.sample(frac=1, replace=True).LogPrice.mean()\n",
    "    for i in range(n)])\n",
    "\n",
    "## Plotting the Distribution of Bootstrapped LogPrice Means \n",
    "plot_hist(LogPrice_bootstrap_means)\n",
    "\n",
    "\n",
    "## Printing out the Values of the Bootstrapped Mean & Std vs Sample Mean & Std \n",
    "print(\"--------------------------\")\n",
    "print(\"Bootstrapping Price Mean: \")\n",
    "print(LogPrice_bootstrap_means.mean())\n",
    "\n",
    "print(\"\\n\")\n",
    "\n",
    "print(\"LogPrice Sample Mean: \")\n",
    "print(Auto.loc[:, \"LogPrice\"].mean())\n",
    "\n",
    "print(\"--------------------------\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence Interval Range:  0.4497717813803394  to  0.5417954967409946\n",
      "--------------------------\n",
      "Bootstrapping Price Std: \n",
      "0.49609793032395044\n",
      "\n",
      "\n",
      "LogPrice Sample Std: \n",
      "0.4975398650134552\n",
      "--------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Bootstrapping the LogPrice Std\n",
    "n = 10000  # going to conduct 10,000 realizations \n",
    "\n",
    "## Bootstrapping the Standard Deviation \n",
    "LogPrice_bootstrap_std = pd.Series([\n",
    "    Auto.sample(frac=1, replace=True).LogPrice.std()\n",
    "    for i in range(n)])\n",
    "\n",
    "\n",
    "## Plotting the Distribution of Bootstrapped LogPrice Standard Deviations   \n",
    "plot_hist(LogPrice_bootstrap_std)\n",
    "\n",
    "\n",
    "## Printing out the Values of the Bootstrapped Mean & Std vs Sample Mean & Std \n",
    "print(\"--------------------------\")\n",
    "print(\"Bootstrapping Price Std: \")\n",
    "print(LogPrice_bootstrap_std.mean()) # mean standard deviation \n",
    "\n",
    "print(\"\\n\")\n",
    "\n",
    "print(\"LogPrice Sample Std: \")\n",
    "print(Auto.loc[:, \"LogPrice\"].std())\n",
    "print(\"--------------------------\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Bayesian Method for Mean & Standard Deviation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Defining functions to calculate posterior & likelihood, mean, and standard deviation\n",
    "\n",
    "def posterior(prior, like):\n",
    "    post = prior * like # compute the product of the probabilities\n",
    "    return post / sum(post) # normalize the distribution to sum to unity\n",
    "\n",
    "def comp_like(p, x): \n",
    "    variance = np.std(x)**2 # sigmasqr\n",
    "    x_mean = np.asarray(x).mean()  # xbar\n",
    "    print('Mean = %.3f, Standard deviation = %.3f' % (x_mean, np.std(x)))\n",
    "    n = len(x)\n",
    "    l = np.exp(-n * np.square(x_mean - p) / (2 * variance))\n",
    "    return l / l.sum()\n",
    "\n",
    "def likelihood(p, data):\n",
    "    k = sum(data)\n",
    "    N = len(data)\n",
    "    # Compute Binomial likelihood\n",
    "    l = scipy.special.comb(N, k) * p**k * (1-p)**(N-k)\n",
    "    # Normalize the likelihood to sum to unity\n",
    "    return l/sum(l)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean = 9.336, Standard deviation = 0.490\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f7f30dcb040>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Creating a Prior Distribution of LogPrice (Mean)\n",
    "\n",
    "N = 10000 \n",
    "p = np.linspace(8, 11, num=N) \n",
    "\n",
    "num_samples = 200 # number of samples from sample dataset \n",
    "Auto_samples = Auto.sample(n=num_samples) # sampling dataset without replacement \n",
    "\n",
    "pp_price = ss.norm.pdf(p, loc=Auto_samples.LogPrice.mean(), \n",
    "                          scale=Auto_samples.LogPrice.std())\n",
    "\n",
    "pp_price = pp_price / pp_price.sum() # normalizing price \n",
    "\n",
    "like_price = comp_like(p, Auto_samples.LogPrice)\n",
    "post_price = posterior(pp_price, like_price)\n",
    "\n",
    "pyplot.plot(p, pp_price, label='prior')\n",
    "pyplot.plot(p, like_price, label='likelihood', alpha=.3, linewidth=10)\n",
    "pyplot.plot(p, post_price, label='posterior')\n",
    "pyplot.legend()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Analysis of Mean & Standard Deviations from Bootstrapping vs Bayesian Method \n",
    "\n",
    "When Bootstrapping the mean of LogPrice (10000 samples), the bootstrapped mean was 9.3475 where the sample mean was 9.3479. There is a very small difference between the two (about 0.0004), which means the sample mean is quite close to the boostrapped mean of 10000 samples.  The 95% confidence interval for this is 9.2793 to 9.4166.  \n",
    "\n",
    "When Bootstrapping the standard deviation (10000 samples), the bootstrapped standard deviation was 0.4956 and the sample standard deviation was 0.4975. There is a smalled difference between the two, specifically 0.0019 difference. The 95% confidence interval for this is 0.4486 to 0.5411. \n",
    "\n",
    "When applying the Bayseian Method, the posterior distribution has 9.350 mean, which is very close to the bootstrapped mean (specifically 9.3475). \n",
    "\n",
    "This shows that both Bootstrapping and applying the Bayesian method will provide means that are relatively close to one another."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.) Compute confidence intervals for the summary statistics by classical bootstrap and Bayesian methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence Interval Range - Bootstrapping Method: \n",
      " 9.28100323171516  to  9.415390558974442\n"
     ]
    }
   ],
   "source": [
    "## Bootstrapping Confidence Interval (calculated initially above)\n",
    "print(\"Confidence Interval Range - Bootstrapping Method: \\n\", \n",
    "  np.percentile(LogPrice_bootstrap_means, (5/2.)),\" to \" , \n",
    "  np.percentile(LogPrice_bootstrap_means, 100-(5/2.))\n",
    "       )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The 0.950 credible interval is 0.025 to 0.975 \n",
      "\n",
      "The confidence interval for Bayesian method is from \n",
      " 9.270027002700271  to  9.403540354035403\n"
     ]
    },
    {
     "data": {
      "image/png": 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zG9M7pzO9czp9g33s7N851lUy26scVMzqaHvfdvbp2Id9p+wL4HkVazoOKmZ19OquV5nWPo3pndkJsh1UrNk4qJjV0fZdWU+lEFS29Xqy3pqLg4pZnewa2EXfYF82/NWZDX/5CDBrNg4qZnWyfdd2AKZ1TGNaxzQAdvTtGMsqme11DipmdfLqrlcB2KdjH6a1Z0Fle9/2sayS2V7noGJWJ4UAMq19GlPbpwLuqVjzcVAxq5PinkohqBSGxMyahYOKWZ14TsXMQcWsbop7KlPapgAOKtZ8HFTM6qR4TqVFLUxtn+qJems6DipmdVLcUwGY2j7VPRVrOg0NKpLOkLRW0jpJl5VZL0lXpfUPSZpfLa+kv0xpH5B0u6RDitZ9KqVfK+n0RrbNrFTxnApkPRb3VKzZNCyoSGoFrgYWAvOA8yXNK0m2EJibbouBa3Lk/XxEHBsRxwE/AD6b8swDzgOOBs4AvpzKMdsr3FMxa2xP5XhgXUSsj4hdwI3AopI0i4DrI7MSmCHp4Ep5I6L4DH3TgCgq68aI6I2Ip4F1qRyzvWJ733Za1EJnayeQBRUfUmzNppFBZRbwXNHzDWlZnjQV80q6QtJzwAdJPZWc20PSYkmrJa3u7u4eUYPMKunp66GrrQtJQDYM5p6KNZtGBhWVWVZ6Gbzh0lTMGxGfiYjZwDeBS0ewPSLi2ohYEBELZs6cWbbiZqOxs3/na4cSg4e/rDk1MqhsAGYXPT8UeD5nmjx5Ab4FnDOC7Zk1TE9/D13tXa8990S9NaNGBpVVwFxJcyR1kE2iLy9Jsxy4IB0FdiKwLSI2VcoraW5R/rOAx4vKOk9Sp6Q5ZJP/9zWqcWal3FMxg7ZGFRwR/ZIuBW4DWoGvRsQaSUvS+qXACuBMskn1HcDFlfKmoq+UdBQwCPwCKJS3RtIy4FGgH7gkIgYa1T6zUuWCiifqrdk0LKgARMQKssBRvGxp0eMALsmbNy0/p0zywrorgCtGW1+zWvT0ZxP1BV1tXezs3zmGNTLb+/yPerM6Ke2pTGmb4qBiTcdBxaxOygWVvsE+BgY9CmvNw0HFrE56+oYe/VV43DvQO1ZVMtvrHFTM6qRcT6Ww3KxZOKiY1clwQaWnr2esqmS21zmomNVJ6dFf7qlYM3JQMauT0p5KIcA4qFgzcVAxq5Od/TvdU7Gm56BiVgcDgwPsGtjliXpreg4qZnVQOGy47ER9vyfqrXk4qJjVQaE3Uu5/Ku6pWDNxUDGrg8Jhwx7+smbnoGJWB4XA4aBizc5BxawOXhv+8tFf1uQcVMzqoDAZX+5/Kv5HvTUTBxWzOvDwl1nGQcWsDsod/dXZ1jlknVkzcFAxq4NyR3+1tbTR1tLmoGJNxUHFrA7KDX+BLylszaehQUXSGZLWSlon6bIy6yXpqrT+IUnzq+WV9HlJj6f0t0iakZYfIalH0gPptrSRbTMrVu7oL8iCjP9Rb82kYUFFUitwNbAQmAecL2leSbKFwNx0WwxckyPvHcAxEXEs8ATwqaLynoqI49JtSWNaZranckd/FZ67p2LNpJE9leOBdRGxPiJ2ATcCi0rSLAKuj8xKYIakgyvljYjbI6I/5V8JHNrANpjlMtzwl4OKNZtGBpVZwHNFzzekZXnS5MkL8N+AW4uez5H0c0l3SzqpXKUkLZa0WtLq7u7ufC0xq6IwUV989Bc4qFjzaWRQUZllkTNN1bySPgP0A99MizYBh0XEW4GPA9+SNH2PQiKujYgFEbFg5syZVZpglk8hcHS2dg5Z3tXuiXprLm0NLHsDMLvo+aHA8znTdFTKK+lC4D3AuyIiACKiF+hNj++X9BTwJmB1PRpjVsnO/p20t7TT2tI6ZLkn6q3ZNLKnsgqYK2mOpA7gPGB5SZrlwAXpKLATgW0RsalSXklnAJ8EzoqIHYWCJM1ME/xIOpJs8n99A9tn9pqe/p49hr7Aw1/WfBrWU4mIfkmXArcBrcBXI2KNpCVp/VJgBXAmsA7YAVxcKW8q+ktAJ3CHJICV6Uivk4HPSeoHBoAlEbG1Ue0zK1Z6ffqCKW1T2LJ9yxjUyGxsNHL4i4hYQRY4ipctLXocwCV586blbxwm/c3AzbXU12y0hgsqXW1dPqGkNRX/o96sDnr6e/b44yNkPZXCpYbNmoGDilkdVBr+8pyKNRMHFbM6cFAxyziomNXBzv6dPvrLDAcVs7rY2b9zjz8+wu6gkv5OZTbpOaiY1UGl4S+AXQO79naVzMaEg4pZHfT291YMKh4Cs2bhoGJWBzv7d752+eBiDirWbBxUzOpgZ/9OprS6p2LmoGJWB70DHv4yAwcVs7rw8JdZxkHFrEYRUfXoLwcVaxYOKmY16hvsA/a8lHDxMgcVaxYOKmY1Gu6qj+CgYs3HQcWsRoWA4Z6KmYOKWc16+7NT2zuomDmomNXsteEvH/1l5qBiVqs8w189/b76ozUHBxWzGhWu7OjhLzMHFbOa+egvs90aGlQknSFpraR1ki4rs16SrkrrH5I0v1peSZ+X9HhKf4ukGUXrPpXSr5V0eiPbZlZQaaK+EGgcVKxZNCyoSGoFrgYWAvOA8yXNK0m2EJibbouBa3LkvQM4JiKOBZ4APpXyzAPOA44GzgC+nMoxa6hKcyqS6GztdFCxppErqEi6WdLvShpJEDoeWBcR6yNiF3AjsKgkzSLg+sisBGZIOrhS3oi4PSL6U/6VwKFFZd0YEb0R8TSwLpVj1lCVgkphuYOKNYu8QeIa4PeBJyVdKenXc+SZBTxX9HxDWpYnTZ68AP8NuHUE20PSYkmrJa3u7u7O0QyzygoT9eUOKQYHFWsuuYJKRPwoIj4IzAeeAe6Q9B+SLpbUPkw2lSsqZ5qqeSV9BugHvjmC7RER10bEgohYMHPmzDJZzEbGPRWz3XIPZ0naH7gI+CPg58A/kAWZO4bJsgGYXfT8UOD5nGkq5pV0IfAe4IMRUQgcebZnVncOKma75Z1T+S5wDzAVeG9EnBURN0XEnwD7DJNtFTBX0hxJHWST6MtL0iwHLkhHgZ0IbIuITZXySjoD+CRwVkTsKCnrPEmdkuaQTf7fl6d9ZrUoHP1V7pBicFCx5tKWM90/RcSK4gWSOtOk+IJyGSKiX9KlwG1AK/DViFgjaUlavxRYAZxJNqm+A7i4Ut5U9JeATrIhOICVEbEklb0MeJRsWOySiBjI2T6zUXNPxWy3vEHlr8gCQLGfkg1/DSsFohUly5YWPQ7gkrx50/I3VtjeFcAVlepkVm+FgNHR2lF2vYOKNZOKQUXSr5EdQdUl6a3sngyfTjYUZtb0egd66WztJPWc9zClbQov7Xxp71bKbIxU66mcTjY5fyjwd0XLXwE+3aA6mU0ow11KuMA9FWsmFYNKRFwHXCfpnIi4eS/VyWxCcVAx263a8NeHIuIbwBGSPl66PiL+rkw2s6bSO9A77B8fwUHFmku14a9p6X64w4bNmp57Kma7VRv++kq6/4u9Ux2zicdBxWy3vH9+/BtJ0yW1S7pT0guSPtToyplNBL39vcP+8REcVKy55D1Ny2kR8TLZqVE2AG8C/mfDamU2geTpqfQO9LL7jEJmk1feoFI4aeSZwA0RsbVB9TGbcPIEFdh9NmOzySxvUPlXSY8DC4A7Jc0E3J83I9/RX+CrP1pzyHvq+8uA3wIWREQfsJ09L7hl1pTy9lQcVKwZ5D33F8Cbyf6vUpzn+jrXx2zCcVAx2y1XUJH0deANwANA4cy/gYOKWa6jv8BBxZpD3p7KAmBe+PAVsz24p2K2W96J+keAX2tkRcwmKgcVs93y9lQOAB6VdB/w2nGREXFWQ2plNoH0DvQ6qJgleYPK5Y2shNlE1T/YT/9gv+dUzJJcQSUi7pZ0ODA3In4kaSrZZX7Nmlrh+vTuqZhl8p7768PAd4CvpEWzgO81qE5mE0bhX/IOKmaZvBP1lwDvAF4GiIgngQOrZZJ0hqS1ktZJuqzMekm6Kq1/SNL8anklfUDSGkmDkhYULT9CUo+kB9Jtac62mY1aIVD4H/VmmbxzKr0RsatwDe70B8iKhxdLagWuBt5NdhLKVZKWR8SjRckWAnPT7QTgGuCEKnkfAc5md6+p2FMRcVzONpnVrBAo3FMxy+Ttqdwt6dNAl6R3A98G/rVKnuOBdRGxPiJ2ATey56ldFgHXR2YlMEPSwZXyRsRjEbE2Z73NGspzKmZD5Q0qlwHdwMPAHwMrgD+vkmcW8FzR8w1pWZ40efKWM0fSzyXdLemkcgkkLZa0WtLq7u7uHEWaDe+14S8f/WUG5D/6a1DS94DvRUTeb2KVKypnmjx5S20CDouIFyX9JvA9SUen68DsLiTiWuBagAULFvgMAVaTPMNfhYDjoGLNoGJPJU2kXy7pBeBxYK2kbkmfzVH2BmB20fNDgedzpsmTd4iI6I2IF9Pj+4GnyC4mZtYweY7+kkRna6eDijWFasNfHyU76uttEbF/ROxHNqH+Dkkfq5J3FTBX0hxJHcB5wPKSNMuBC1LwOhHYFhGbcuYdQtLMNMGPpCPJJv/XV6mjWU3yHP0FvqSwNY9qQeUC4PyIeLqwICLWAx9K64YVEf3ApcBtwGPAsohYI2mJpCUp2QqyL/51wD8C/6NSXgBJ75e0gez6Lj+UdFsq62TgIUkPkv2nZomvUGmN1tPXA0BXW1fFdA4q1iyqzam0R8QLpQsjoltSe7kMJelWkAWO4mVLix4H2X9gcuVNy28Bbimz/Gbg5mp1Mqunnv4UVNodVMygek9l1yjXmTUF91TMhqrWU3mLpJfLLBcw/MykWZNwT8VsqIpBJSJ80kizCtxTMRsq758fzawM91TMhnJQMatBT18PHa0dtKjyR8lBxZqFg4pZDXb07ag69AUOKtY8HFTMatDT31N16AscVKx5OKiY1aCnv8c9FbMiDipmNejpc0/FrJiDilkN3FMxG8pBxawG7qmYDeWgYlaDkfRUegd6q14UyGyic1Axq8FIeioAEYONrpLZmHJQMavBSHoqAIMOKjbJOaiY1WCkPRUHFZvsHFTMauCeitlQDipmNejpc1AxK+agYjZKwchO0wIOKjb5OaiYjVJEMBiD7qmYFXFQMRulwRgAql9LBXYHlQEHFZvkGhpUJJ0haa2kdZIuK7Nekq5K6x+SNL9aXkkfkLRG0qCkBSXlfSqlXyvp9Ea2zazQ68jTU5naPjXlGWhonczGWsOCiqRW4GpgITAPOF/SvJJkC4G56bYYuCZH3keAs4Efl2xvHnAecDRwBvDlVI5ZQxR6HXl6KtPap2V5Bt1TscmtkT2V44F1EbE+InYBNwKLStIsAq6PzEpghqSDK+WNiMciYm2Z7S0CboyI3oh4GliXyjFriNeGv3L0VKZ1pKDinopNco0MKrOA54qeb0jL8qTJk3c020PSYkmrJa3u7u6uUqTZ8AZH0VPx8JdNdo0MKiqzrPR8esOlyZN3NNsjIq6NiAURsWDmzJlVijQbXmEoa0Q9lUEHFZvc2hpY9gZgdtHzQ4Hnc6bpyJF3NNszq5tCr2Ofjn2qpu1q60LIR3/ZpNfInsoqYK6kOZI6yCbRl5ekWQ5ckI4COxHYFhGbcuYttRw4T1KnpDlkk//31bNBZsUK8yOFXkglkpjaPtU9FZv0GtZTiYh+SZcCtwGtwFcjYo2kJWn9UmAFcCbZpPoO4OJKeQEkvR/4IjAT+KGkByLi9FT2MuBRoB+4JMID2NY4hQCRp6cCWfDxnIpNdo0c/iIiVpAFjuJlS4seB3BJ3rxp+S3ALcPkuQK4ooYqm+VWGMoqTMJXM619GgOxvZFVMhtz/ke92SiNpqfi/6nYZOegYjZKAyM4TQsUeioe/rLJzUHFbJQGY4Bp7dNoUb6PkedUrBk4qJiN0sDgQK4jvwqmtU/z0V826TmomI3SQOqp5DWtY5r/p2KTnoOK2SgNDA7knqQHz6lYc3BQMRulgRgc8fDXoIe/bJJzUDEbpYEYYU+lwz0Vm/wcVMxGaWBwhHMq7dOIgMGodm5Us4nLQcVslAZH0VMBX1PFJjcHFbNRGk1PBXxNFZvcHFTMRmkgRvg/FV9TxZqAg4rZKATZRbpGMvz1uo7XAdDvoGKTmIOK2SiM5AJdBdM7pwMwEP0NqZPZeOCgYjYKhd7Gvp375s6z75R9h+Q1m4wcVMxGoX8w620UAkUehQBUyGs2GTmomI3CQCGojKKnMuCgYpOYg4rZKIymp1KYU/Hwl01mDipmo1AIDIVAkUdbSxutLS0e/rJJraFBRdIZktZKWifpsjLrJemqtP4hSfOr5ZW0n6Q7JD2Z7l+flh8hqUfSA+m2tJFts+bWP4rhL4BWtfnoL5vUGhZUJLUCVwMLgXnA+ZLmlSRbCMxNt8XANTnyXgbcGRFzgTvT84KnIuK4dFvSmJaZ7T4seCTDXwBtLa3uqdik1sieyvHAuohYHxG7gBuBRSVpFgHXR2YlMEPSwVXyLgKuS4+vA97XwDaYlVUY/hrJ/1QgGwLznIpNZo0MKrOA54qeb0jL8qSplPegiNgEkO4PLEo3R9LPJd0t6aRylZK0WNJqSau7u7tH2iYzIBv+amtpzX19+oLWljYf/WWTWiODisosKz3n93Bp8uQttQk4LCLeCnwc+JakPWZRI+LaiFgQEQtmzpxZpUiz8gYG+2ltaRtxvqyn4qBik1cjg8oGYHbR80OB53OmqZR3cxoiI91vAYiI3oh4MT2+H3gKeFNdWmJWIuupjCaotHr4yya1RgaVVcBcSXMkdQDnActL0iwHLkhHgZ0IbEtDWpXyLgcuTI8vBL4PIGlmmuBH0pFkk//rG9c8a2ajDyruqdjkNvJPRU4R0S/pUuA2oBX4akSskbQkrV8KrADOBNYBO4CLK+VNRV8JLJP0h8CzwAfS8pOBz0nqBwaAJRGxtVHts+bWN9hHV9vUEedra2lnMAbp6euhq72rATUzG1sNCyoAEbGCLHAUL1ta9DiAS/LmTctfBN5VZvnNwM01Vtksl76BPqZ3to84X0drlueFHS8we9/ZVVKbTTz+R73ZCEUEfYN9tLeMPKgU8nTv8JGHNjk5qJiN0Mu9LxMB7a2jCCopT/d2BxWbnBxUzEbohR0vANTUUymUYTbZOKiYjdBrQWVUPZUOwMNfNnk5qJiNUC09lbaWNiQPf9nk5aBiNkJbtm8BRtdTEdlhxR7+ssnKQcVshDa+shGAjjSUNVIdre1s2bGlnlUyGzccVMxGaOPLG2lvbaN1hCeTLOho7WTjyxvrXCuz8cFBxWyENr6ykY7WzlHnn9LWybPbnq1jjczGDwcVsxHa+MpGOmsIKp2tU9i8fTO9/b11rJXZ+OCgYjZCG1/eSGfb6OZTIOupAGx4eUO9qmQ2bjiomI3Ajr4dbN6+mc7WKaMuo7Mty+shMJuMHFTMRmDd1nUATK3hDMOFnsovtv2iLnUyG08cVMxG4IkXnwCgq33kp70v6GydQntLO4+/8Hi9qmU2bjiomI3Aky8+CUBX2+h7Ki0SRx1wFGu611RPbDbBOKiYjcCDmx9k9vTZtLW01lTOMQcewyNbHqlTrczGDwcVsxFY9fwq3jbrbTWX8xsH/gbPvPQMv+r5VR1qZTZ+OKiY5dS9vZv1v1rP2w6pPai887B3AvDjX/y45rLMxhMHFbOcbl13KwCnHnlqzWWdMOsEutq6uPPpO2suy2w8cVAxy2nZmmUcvM/BzD94fs1ldbZ18u43vJtla5bRN9BXh9qZjQ8NDSqSzpC0VtI6SZeVWS9JV6X1D0maXy2vpP0k3SHpyXT/+qJ1n0rp10o6vZFts+by4C8f5IdP/pAPz/8wLaM8kWSpD8//MJu3b+b6B6+vS3lm40HDgoqkVuBqYCEwDzhf0rySZAuBuem2GLgmR97LgDsjYi5wZ3pOWn8ecDRwBvDlVI7ZqA0MDnDvs/dy9rKzOWjaQXzkhI/Urewz557JSYedxJ/+25+ybM0ynwvMJoW2BpZ9PLAuItYDSLoRWAQ8WpRmEXB9RASwUtIMSQcDR1TIuwg4JeW/DrgL+GRafmNE9AJPS1qX6vDTejfs4c0Pc+53zh2yLIihzyNqWj+ZyihdP5HK2DWwi96BXg6cdiDLz1vO/lP336OM0WpRCzf93k0s/OZCzv3OubS3tHPA1AOY2j6VFrUgKbtHSKrbds0AFr5xIV847Qt1L7eRQWUW8FzR8w3ACTnSzKqS96CI2AQQEZskHVhU1soyZQ0haTFZr4jDDjtsBM3Zrau9i2MOPGaP5aUffKGa1o9ZGZQpY7K0bYRltKqVYw86lve/+f3s07HPHnlrdfDrDmb14tWseHIFKzesZMv2LfT09xARDMYgQXZvVm+zXrfH12NdNDKolPtpVfpTcbg0efKOZntExLXAtQALFiyoVmZZb9zvjSz7wLLRZDXbQ1tLG2cddRZnHXXWWFfFrGaNnKjfAMwuen4o8HzONJXybk5DZKT7wnVZ82zPzMwaqJFBZRUwV9IcSR1kk+jLS9IsBy5IR4GdCGxLQ1uV8i4HLkyPLwS+X7T8PEmdkuaQTf7f16jGmZnZnho2/BUR/ZIuBW4DWoGvRsQaSUvS+qXACuBMYB2wA7i4Ut5U9JXAMkl/CDwLfCDlWSNpGdlkfj9wSUQMNKp9Zma2p0bOqRARK8gCR/GypUWPA7gkb960/EXgXcPkuQK4ooYqm5lZDfyPejMzqxsHFTMzqxsHFTMzqxsHFTMzqxuVO3VFs5DUDfyihiIOAF6oU3XG0mRpB7gt49FkaQe4LQWHR8TMciuaOqjUStLqiFgw1vWo1WRpB7gt49FkaQe4LXl4+MvMzOrGQcXMzOrGQaU21451BepksrQD3JbxaLK0A9yWqjynYmZmdeOeipmZ1Y2DipmZ1Y2DShWSPiZpjaRHJN0gaUrJekm6StI6SQ9Jmj9Wda0mR1tOkbRN0gPp9tmxqms1kv40tWONpI+WWT8h9kuOdozbfSLpq5K2SHqkaNl+ku6Q9GS6f/0wec+QtDbtn8v2Xq3Lq7Etz0h6OO2f1Xuv1uUN05YPpPfYoKRhDyOuy36JCN+GuZFdjvhpoCs9XwZcVJLmTOBWsitPngj851jXu4a2nAL8YKzrmqMtxwCPAFPJzrT9I2DuRNsvOdsxbvcJcDIwH3ikaNnfAJelx5cBf10mXyvwFHAk0AE8CMybiG1J654BDhjr/VGlLW8GjgLuAhYMk68u+8U9leragC5JbWQf/tKrSS4Cro/MSmBG4cqU41C1tkwUbwZWRsSOiOgH7gbeX5JmIuyXPO0YtyLix8DWksWLgOvS4+uA95XJejywLiLWR8Qu4MaUb8zU0JZxp1xbIuKxiFhbJWtd9ouDSgURsRH4AtnFwDaRXZny9pJks4Dnip5vSMvGlZxtAfgtSQ9KulXS0Xu1kvk9ApwsaX9JU8l6JbNL0kyE/ZKnHTAx9knBQZFdvZV0f2CZNBNh30C+tgAEcLuk+yUt3mu1q7+67BcHlQrSGOoiYA5wCDBN0odKk5XJOu6O087Zlp+RndPnLcAXge/t1UrmFBGPAX8N3AH8G1k3vb8k2bjfLznbMSH2yQiN+30zQu+IiPnAQuASSSePdYVGqS77xUGlslOBpyOiOyL6gO8Cby9Js4Ghvy4PZXwOK1VtS0S8HBGvpscrgHZJB+z9qlYXEf8cEfMj4mSyrv6TJUkmxH6p1o6JtE+SzYVhxnS/pUyaCbFvyNcWIuL5dL8FuIVsGGkiqst+cVCp7FngRElTJYnsMsaPlaRZDlyQjjY6kWxYadPermgOVdsi6dfSOiQdT/b+eHGv1zQHSQem+8OAs4EbSpJMiP1SrR0TaZ8ky4EL0+MLge+XSbMKmCtpjqQO4LyUb7yp2hZJ0yS9rvAYOI1sWHMiqs9+GesjFcb7DfgL4HGyN8rXgU5gCbAkrRdwNdlREw8zzJEV4+GWoy2XAmvIhmFWAm8f6zpXaMs9wKOpru9KyybcfsnRjnG7T8gC4Cagj+xX7h8C+wN3kvW47gT2S2kPAVYU5T0TeCLtn89M1LaQHSn1YLqtGcdteX963AtsBm5r1H7xaVrMzKxuPPxlZmZ146BiZmZ146BiZmZ146BiZmZ146BiZmZ146BiTUvSQDqz7COSvp1OlTLWdTpFUukfbBu9zSOKz2hrVgsHFWtmPRFxXEQcA+wi+39IVemEnI1yCnuetaGiBtfHbEQcVMwy9wBvlPReSf8p6eeSfiTpIABJl0u6VtLtwPXp1/09kn6Wbm9P6U6RdLekZZKekHSlpA9Kui9dc+MNKd1MSTdLWpVu75B0BFlg+1jqQZ1ULl25+hQ3RNJNks4sev41SecMV+eSvBdJ+lLR8x9IOiU9Pk3ST1Peb0vap547wCYH/8Kxppd+6S8kO6njvcCJERGS/gj4X8AnUtLfBN4ZET1pqOzdEbFT0lyyfzEXLn70FrLT2m8F1gP/FBHHS/pT4E+AjwL/APx9RNybTtFyW0S8WdJS4NWI+EKq27dK06Wyh9SnpEk3AucCK9LpNt4F/HeyswwMV+dqr9EBwJ8Dp0bEdkmfBD4OfC5PfmseDirWzLokPZAe3wP8M9mFjG5KJxDsILuwWcHyoi/wduBLko4DBoA3FaVbFek8Y5KeAgqXGHgY+J30+FRgXjqtF8D0wjmkSlRKt7xMQIHs4mRXSeoEzgB+nALhvhXqXM2JwDzgJ6kuHcBPR5DfmoSDijWznog4rniBpC8CfxcRy9Owz+VFq7cXPf4Y2TmU3kI2jLyzaF1v0ePBoueD7P7MtQC/VRoUioIHOdJtL00MkHoidwGnk/VYCieprFTngn6GDosXLjkt4I6IOL/cNs0KPKdiNtS+wMb0+MIq6TZFxCDwB2SXYh2J28lOFglA6j0AvAK8Lke6am4ELgZOIhsyy1vnZ4DjJLVIms3u07ivBN4h6Y2pHlMljaSnY03CQcVsqMuBb0u6B3ihQrovAxdKWkk2jFS211DBR4AFkh6S9Ci7jzz7V+D9hYn6CumquZ3sWuU/iuzSsHnr/BOyIb+Hya4U+jOAiOgGLgJukPQQWZD59ZE02JqDz1JsZmZ1456KmZnVjYOKmZnVjYOKmZnVjYOKmZnVjYOKmZnVjYOKmZnVjYOKmZnVzf8DTRpW8Py7r1gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Bayesian Credible Intervals \n",
    "num_samples = 10000\n",
    "lower_q, upper_q = [.025, .975]\n",
    "\n",
    "def plot_ci(p, post, num_samples, lower_q, upper_q):\n",
    "    ## This function computes a credible interval using an assumption\n",
    "    ## of symetry in the bulk of the distribution to keep the calculation simple. \n",
    "    ## Compute a large sample by resampling with replacement\n",
    "    samples = np.random.choice(p, size=num_samples, replace=True, p=post)\n",
    "    ci = np.percentile(samples, [lower_q*100, upper_q*100]) # compute the quantiles\n",
    "    \n",
    "    interval = upper_q - lower_q\n",
    "    pyplot.title('Posterior density with %.3f credible interval' % interval)\n",
    "    pyplot.plot(p, post, color='green')\n",
    "    pyplot.xlabel('Parameter value')\n",
    "    pyplot.ylabel('Density')\n",
    "    pyplot.axvline(x=ci[0], color='red')\n",
    "    pyplot.axvline(x=ci[1], color='red')\n",
    "    print('The %.3f credible interval is %.3f to %.3f \\n' \n",
    "          % (interval, lower_q, upper_q))\n",
    "    print(\"The confidence interval for Bayesian method is from \\n\"\n",
    "          , ci[0], \" to \", ci[1])\n",
    "    \n",
    "plot_ci(p, post_price, num_samples, lower_q, upper_q)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Analysis of CI from Bootstrapping vs Bayesian Method \n",
    "\n",
    "The 95% confidence interval from Bootstrapping is 9.279 to 9.416. The 95% confidence interval from the Bayesian method is 9.282 to  9.421. These are very close to one another and show that regardless of using Bootstrapping or the Bayesian method, one can produce very similar results for the analysis they are conducting. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.) Correctly use hypothesis tests to determine if the differences in pairs and multiple populations are statistically significant. You will continue the analysis that you started in Assignment 04. For each of the groupings you analyzed in Assignment 04, apply the following methods:\n",
    "\n",
    "   -  Bootstrap methods\n",
    "   -  Bayesian model\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Defining Functions to assist conducting the T-test and Plotting Results \n",
    "\n",
    "## Histogram Plot \n",
    "def hist_plot(vec, bins):\n",
    "    import matplotlib.pyplot as plt\n",
    "    from statistics import mean\n",
    "    plt.hist(vec, bins = bins)\n",
    "    plt.axvline(mean(vec), color = 'red')\n",
    "    plt.ylabel('Frequency')\n",
    "    plt.xlabel('Value')\n",
    "    \n",
    "## Confidence Interval on Histogram \n",
    "def hist_mean_ci(vec, t_test, bins):\n",
    "    import matplotlib.pyplot as plt\n",
    "    from statistics import mean\n",
    "    upper = mean(vec) + t_test[5] - t_test[1]\n",
    "    lower = mean(vec) + t_test[4] - t_test[1]\n",
    "    plt.hist(vec, bins = bins)\n",
    "    plt.axvline(mean(vec), color = 'red')\n",
    "    plt.axvline(upper, color = 'red', linestyle='--')\n",
    "    plt.axvline(lower, color = 'red', linestyle='--')\n",
    "    plt.ylabel('Frequency')\n",
    "    plt.xlabel('Value')\n",
    "    \n",
    "## Function to Plot T-Tests \n",
    "def plot_t(a, b, t_test, cols=['A', 'B'], nbins = 20):\n",
    "    import matplotlib.pyplot as plt\n",
    "    plt.figure(figsize=(7, 8))\n",
    "    minx = min([min(a), min(b)])\n",
    "    maxx = max([max(a), max(b)])\n",
    "    stepx = (maxx - minx)/(nbins + 1)\n",
    "    bins = [minx + i * stepx for i in range(nbins + 1)]\n",
    "    plt.subplot(2, 1, 1) # The first plot\n",
    "    hist_mean_ci(a, t_test, bins)\n",
    "    plt.title('Histogram of ' + cols[0] + ' and ' + cols[1])\n",
    "    plt.subplot(2, 1, 2) # The next plot\n",
    "    hist_plot(b, bins)\n",
    "    \n",
    "## Function for Non-paired T Tests\n",
    "def t_test(a, b, alpha, alternative='two-sided'):\n",
    "    from scipy import stats\n",
    "    import scipy.stats as ss\n",
    "    import pandas as pd\n",
    "    import statsmodels.stats.weightstats as ws\n",
    "    \n",
    "    diff = a.mean() - b.mean()\n",
    "\n",
    "    res = ss.ttest_ind(a, b, equal_var=False)\n",
    "      \n",
    "    means = ws.CompareMeans(ws.DescrStatsW(a), ws.DescrStatsW(b))\n",
    "    confint = means.tconfint_diff(alpha=alpha, alternative=alternative, usevar='unequal') \n",
    "    degfree = means.dof_satt()\n",
    "\n",
    "    index = ['DegFreedom', 'Difference', 'Statistic', 'PValue', 'Low95CI', 'High95CI']\n",
    "    return pd.Series([degfree, diff, res[0], res[1], confint[0], confint[1]], index = index)   \n",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--------------------------\n",
      "Bootstrapping Aspiration=Std Price Mean: \n",
      "9.290011781277\n",
      "--------------------------\n",
      "Bootstrapping Aspiration=Turbo Price Mean: \n",
      "9.612760621120625\n"
     ]
    }
   ],
   "source": [
    "### Bootstrapping Aspiration=Std Column \n",
    "\n",
    "n = 1000  # going to conduct 1,000 realizations \n",
    "\n",
    "# Separating the categories for Aspiration: \n",
    "std = Auto.loc[Auto.loc[:, 'aspiration'] == 'std', 'LogPrice']\n",
    "turbo = Auto.loc[Auto.loc[:, 'aspiration'] == 'turbo', 'LogPrice']\n",
    "\n",
    "## Bootstrapping the Mean of the Standard Aspiration\n",
    "std_bootstrap_mean = pd.Series([\n",
    "    std.sample(frac=1, replace=True).mean()\n",
    "    for i in range(n)])\n",
    "\n",
    "\n",
    "# ## Plotting the Distribution of Bootstrapped Aspiration=Std mean \n",
    "# plot_hist(std_bootstrap_mean)\n",
    "\n",
    "\n",
    "## Printing out the Values of the Bootstrapped Means\n",
    "print(\"--------------------------\")\n",
    "print(\"Bootstrapping Aspiration=Std Price Mean: \")\n",
    "print(std_bootstrap_mean.mean()) \n",
    "\n",
    "######################################################\n",
    "## Bootstrapping the Mean of the Turbo Aspiration \n",
    "turbo_bootstrap_mean = pd.Series([\n",
    "    turbo.sample(frac=1, replace=True).mean()\n",
    "    for i in range(n)])\n",
    "\n",
    "# ## Plotting the Distribution of Bootstrapped Turbo Aspiration Means  \n",
    "# plot_hist(turbo_bootstrap_mean)\n",
    "\n",
    "\n",
    "## Printing out the Values of the Bootstrapped Means\n",
    "print(\"--------------------------\")\n",
    "print(\"Bootstrapping Aspiration=Turbo Price Mean: \")\n",
    "print(turbo_bootstrap_mean.mean()) # mean \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DegFreedom    1667.097727\n",
      "Difference      -0.322749\n",
      "Statistic     -136.819197\n",
      "PValue           0.000000\n",
      "Low95CI         -0.327376\n",
      "High95CI        -0.318122\n",
      "dtype: float64\n"
     ]
    },
    {
     "data": {
      "image/png": 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zJ8CCiDi/4qObgJPT6ZOBGyviEyVtKmkXYBQwZyCNsdou+NX3uOBX36sZMzMroqw9vTuAw4BV6fxQ4Hbgff2scxDwKeBRSXPT2BTgPGCGpFOAZ4ATACJivqQZwGMkZ36eHhFrszfFshi+8rlMMTOzIspa9DaLiJ6CR0Ss6unp9SUifk/143QAh/axzlRgasaczMzMBiTr8ObLkvbvmZF0APBKP8ubmZkNOll7emcB10jqObFkOPCxXDIyMzPLSaaiFxH3S9oD2J1kyHJhRLyWa2aWiwdH7JEpZmZWRAO54fSBQHu6zn6SiIif5pKV5eY/PviZTDEzsyLKenH6z4DdgLlAzxmVAbjomZlZy8ja0+sARkeELwZvcRdf/x0AvjBhSr8xM7Miylr05gFvB5bmmIs1wLavrMgUMzMroqxFbxjwmKQ5wOqeYER8JJeszMzMcpC16J2bZxJmZmaNkPWShbskvQMYFRF3pHdj8QNezcyspWQ9e/NUksf5bEdyFucI4BL6uJ2YDV53v2PfTDEzsyLKOrx5OslTzO+Dvz9Qdvv+V7HB6D8POilTzMysiLLee3N1RLzaMyNpY6o84NXMzGwwy1r07pI0Bdhc0oeBa4Bf5ZeW5WX6jG8yfcY3a8bMzIooa9GbDHQDjwKfB24F+nxiug1em61ZzWZrVteMmZkVUdazN18HLk1fZmZmLSnr2ZtPUeUYXkTsWveMzMzMcjKQe2/22Aw4geTyBTMzs5aRdXjz+V6hH0j6PXBO/VOyPM3abWymmJlZEWUd3ty/YnYjkp7fVrlkZLm69N0fzRQzMyuirMOb36+YXgMsBk6sezZmZmY5yjq8echANyzpMuAYYHlE7J3GzgVOJbn8AWBKRNyafnY2cArJQ2r/OSJ+M9B9Wm1XXTEZgIkfP6/fmJlZEWUd3vyX/j6PiPOrhKcDF7Lu09UviIjv9dr+aGAisBewI3CHpHdFxFrMzMzqJOvF6R3AF0huND0COA0YTXJcr+qxvYiYDbyQcfvjgasiYnVEPAUsIrnXp5mZWd0M5CGy+0fESvj7MOU1EfFP67HPMyR9GugEvhIRL5IU0nsrlulKY2ZmZnWTtac3Eni1Yv5VoH099ncxyaOJxgBLeeMEGVVZtuoNrSVNktQpqbO7u7vaImZmZlVl7en9DJgj6XqSYjSBdY/V1RQRy3qmJV0K3JzOdgE7Vyy6E7Ckj21MA6YBdHR0+EkPA3TzHh/IFDMzK6KsZ29OlfRroOe342cj4qGB7kzS8IhYms5OAOal0zcBV0g6n+REllHAnIFu32r7+f5HZ4qZmRVR1p4ewFBgRUT8l6Q2SbukJ51UJelKYBwwTFIX8E1gnKQxJL3FxSRPbCAi5kuaATxGch3g6T5zMx+bvfY3AP62yWb9xszMiijrJQvfJDmDc3fgv4BNgJ8DB/W1TkRUexz3T/pZfiowNUs+tv6mX3Mu8OZr8qrFzMyKKOuJLBOAjwAvA0TEEnwbMjMzazFZi96rERGkZ1RK2iK/lMzMzPKRtejNkPQjYBtJpwJ34AfKmplZi6l5TE+SgKuBPYAVJMf1zomImTnnZmZmVlc1i15EhKQbIuIAwIWuxV37Pw7LFDMzK6KslyzcK+nAiLg/12wsdy56ZlZmWYveIcBpkhaTnMEpkk7gPnklZvnY9q9/AeDFoW/tN2ZmVkT9Fj1JIyPiGeDIBuVjObv4hv8PePM1edViZmZFVKundwPJ0xWelnRdRPxjA3IyMzPLRa1LFiqffrBrnomYmZnlrVbRiz6mzczMWk6t4c19Ja0g6fFtnk7DGyeybJ1rdmZmZnXUb9GLiCGNSsQa4+f7HZUpZmZWRAN5tJAVwM17HpwpZmZWRFnvvWkFMXxFN8NXdNeMmZkVkXt6JXPBzd8H3nxNXrWYmVkRuadnZmal4Z6eNUT75Fvqsp3F5x1dl+2YWTm5p2dmZqXhomdmZqXh4c2SuXTshEwxM7Miyq3oSboMOAZYHhF7p7HtSJ7C3g4sBk6MiBfTz84GTgHWAv8cEb/JK7cym/XOd2eKmZkVUZ7Dm9OBI3rFJgOzImIUMCudR9JoYCKwV7rORZJ8N5gc7Pp8F7s+31UzZmZWRLkVvYiYDbzQKzweuDydvhw4riJ+VUSsjoingEXA2LxyK7Pv/OZCvvObC2vGzMyKqNEnsuwQEUsB0vft0/gI4NmK5brS2DokTZLUKamzu9t3ETEzs+wGy9mbqhKr+iijiJgWER0R0dHW1pZzWmZmViSNLnrLJA0HSN+Xp/EuYOeK5XYCljQ4NzMzK7hGX7JwE3AycF76fmNF/ApJ5wM7AqOAOQ3ObYPV664jZmaWjzwvWbgSGAcMk9QFfJOk2M2QdArwDHACQETMlzQDeAxYA5weEWvzyq3M/vN9EzPFzMyKKLeiFxEn9fHRoX0sPxWYmlc+lri7fUymmJlZEQ2WE1msQUYve5LRy56sGTMzKyIXvZI5Z9Y0zpk1rWbMzKyIXPTMzKw0XPTMzKw0XPTMzKw0XPTMzKw0/Dy9kvmPg0/OFDMzKyIXvZJ5cKc9M8XMzIrIw5sls3/XAvbvWlAzZmZWRC56JfO12ZfztdmX14yZmRWRi56ZmZWGi56ZmZWGi56ZmZWGi56ZmZWGL1komX8/dFKmmJlZEbnolcxjO+yaKWZmVkQe3iyZgxbP5aDFc2vGzMyKyD29kjnzD1cBb35aerWYmVkRuadnZmal4aJnZmal0ZThTUmLgZXAWmBNRHRI2g64GmgHFgMnRsSLzcjPzMyKqZk9vUMiYkxEdKTzk4FZETEKmJXOm5mZ1c1gOpFlPDAunb4cuBP4erOSKaoph5+RKWZmVkTNKnoB3C4pgB9FxDRgh4hYChARSyVt36TcCu3Jt+2UKWZmVkTNKnoHRcSStLDNlLQw64qSJgGTAEaOHJlXfoV16KL7AJj1znf3GzMzK6KmFL2IWJK+L5d0PTAWWCZpeNrLGw4s72PdacA0gI6OjmhUzkVx6pzrgTcXuGoxM7MiaviJLJK2kLRVzzTwD8A84Cbg5HSxk4EbG52bmZkVWzN6ejsA10vq2f8VEXGbpPuBGZJOAZ4BTmhCbmZmVmANL3oR8SSwb5X488Chjc7HzMzKw3dkMTOz0hhM1+lZA3z5mK9kipmZFZGLXsks3botU8zMrIg8vFkyxyyYzTELZteMmZkVkXt6JfPJh24F4OY9D+43ZmZWRO7pmZlZabjomZlZabjomZlZabjomZlZafhElpL5wnFnZ4qZmRWRi17JvDj0rZlig1X75Fs2eBuLzzu6DpmYWSvy8GbJHP/oHRz/6B01Y2ZmReSeHvXpPbSKnuJ27f84rN+YmVkRuadnZmal4aJnZmal4aJnZmal4aJnZmal4RNZSuYzJ5ybKWZmVkQueiXzt002yxQzMysiD2+WzCcfvIVPPnhLzZiZWRG56JXMMQt/xzELf1czZmZWRIOu6Ek6QtLjkhZJmtzsfMzMrDgGVdGTNAT4P8CRwGjgJEmjm5uVmZkVxWA7kWUssCgingSQdBUwHnisqVlZodTrtnO+cbVZ6xlUPT1gBPBsxXxXGjMzM9tgiohm5/B3kk4ADo+If0rnPwWMjYgzK5aZBExKZ3cHHm9gisOA5xq4v2YpSzuhPG11O4unLG1dn3a+IyLaqn0w2IY3u4CdK+Z3ApZULhAR04BpjUyqh6TOiOhoxr4bqSzthPK01e0snrK0td7tHGzDm/cDoyTtIuktwETgpibnZGZmBTGoenoRsUbSGcBvgCHAZRExv8lpmZlZQQyqogcQEbcCtzY7jz40ZVi1CcrSTihPW93O4ilLW+vazkF1IouZmVmeBtsxPTMzs9y46FUh6UuS5kmaL+msKp9/QtIj6esPkvZtQpobLEM7x6dtnCupU9L7m5DmBqvVzorlDpS0VtLxDUyvrjJ8p+Mk/SX9TudKOqcJaW6wLN9p2ta56TJ3NTjFusjwff7Piu9yXvrvd7smpLrBMrT1rZJ+JenhdJnPrteOIsKvihewNzAPGEpyzPMOYFSvZd4HbJtOHwnc1+y8c2rnlrwxBL4PsLDZeefRznS5IcBvSY4nH9/svHP8TscBNzc71wa0cxuSOzmNTOe3b3beebSz1/LHAr9tdt45fqdTgO+m023AC8BbBrov9/TWtSdwb0T8NSLWAHcBEyoXiIg/RMSL6ey9JNcTtpos7VwV6b8wYAugFQ8A12xn6kzgOmB5I5Ors6xtbXVZ2vlx4JcR8QxARLTi9zrQ7/Mk4MqGZFZ/WdoawFaSRPIH+QvAmoHuyEVvXfOAgyW9TdJQ4CjefMF8b6cAv25IZvWVqZ2SJkhaCNwCfK7BOdZDzXZKGkHyH+ySJuRXT1n/7b43HSL6taS9GptiXWRp57uAbSXdKekBSZ9ueJYbLvPvovTzI0j+cGtFWdp6IUlxXAI8CnwpIl4f6I4G3SULzRYRCyR9F5gJrAIepo+/JiQdQlL0Wu5YV9Z2RsT1wPWSDga+DRzW0EQ3UMZ2/gD4ekSsTf6IbE0Z2/ogyS2aVkk6CrgBGNXQRDdQxnZuDBwAHApsDtwj6d6I+GNDk90AA/ldRDK0eXdEvNCo/OopY1sPB+YCHwJ2A2ZK+l1ErBjIvtzTqyIifhIR+0fEwSRd6Cd6LyNpH+DHwPiIeL7ROdZDlnZWLDsb2E3SsIYlWCcZ2tkBXCVpMXA8cJGk4xqbZX3UamtErIiIVen0rcAmBf1Ou4DbIuLliHgOmA203AlnA/g/OpHWHdoEMrX1syRD1hERi4CngD3WZ0d+rXtQdfv0fSSwkPSklYrPRwKLgPc1O9ec2/lO3jiRZX/gzz3zrfSq1c5ey06nRU9kyfidvr3iOx0LPFPE75RkGGwWSY9vKMnw2d7Nzrve7Uw/eytJkdii2fnm/J1eDJybTu+Q/j4aNtD9eHizuuskvQ14DTg9Il6UdBpARFwCnAO8jaRHALAmWvPGr7Xa+Y/ApyW9BrwCfCzSf3EtplY7i6RWW48HviBpDcl3OrGI32kkw2W3AY8ArwM/joh5Tcx3fWX5tzsBuD0iXm5WknVSq63fBqZLehQQySGJAT9lwndkMTOz0vAxPTMzKw0XPTMzKw0XPTMzKw0XPTMzKw0XPTMzKw0XPbNBJr111uG9YmdJuqif5VvxkhmzhnPRMxt8riS5w0allr/jhtlg4KJnNvhcCxwjaVMASe3AjsDH0+cazpf0rWorSlpVMX28pOnpdJuk6yTdn74Oyr0VZoOQi57ZIBPJvVznkNw1H5Je3tXAv6Z3/tkH+GB6/9esfghcEBEHktxp58d1TNmsZfg2ZGaDU88Q543p++eAEyVNIvl/OxwYTXKbrSwOA0ZXPEVia0lbRcTKumZtNsi56JkNTjcA50van+TROC8CXwUOTO9JOB3YrMp6lfcVrPx8I+C9EfFKPumatQYPb5oNQpE8/udO4DKSXt/WwMvAXyTtABzZx6rLJO0paSPe/OTp24EzemYkjckhbbNBz0XPbPC6kuQZcFdFxMPAQ8B8kkJ4dx/rTAZuBn4LLK2I/zPQIekRSY8Bp+WWtdkg5qcsmJlZabinZ2ZmpeGiZ2ZmpeGiZ2ZmpeGiZ2ZmpeGiZ2ZmpeGiZ2ZmpeGiZ2ZmpeGiZ2ZmpeGiZ2ZmpdHSN5weNmxYtLe3NzsNM2sFjz+evO++e3PzsNw98MADz0VEW7XPWrrotbe309nZ2ew0zKwVjBuXvN95ZzOzsAaQ9HRfn3l408zMSiO3oidpZ0n/LWmBpPmSvpTGt5M0U9IT6fu2FeucLWmRpMclHZ5XbmZmVk559vTWAF+JiD2B9wCnSxpN8uiTWRExCpiVzpN+NhHYCzgCuEjSkBzzMzOzksmt6EXE0oh4MJ1eCSwARgDjgcvTxS4Hjkunx5M8N2x1RDwFLALG5pWfmZmVT0OO6UlqB/YD7gN2iIilkBRGYPt0sRHAsxWrdaUxMzOzusi96EnaErgOOCsiVvS3aJXYOk+4lTRJUqekzu7u7nqlaWZmJZBr0ZO0CUnB+0VE/DINL5M0PP18OLA8jXcBO1esvhOwpPc2I2JaRHREREdbW9XLMMzMzKrK8+xNAT8BFkTE+RUf3QScnE6fDNxYEZ8oaVNJuwCjgDl55WdmZuWT58XpBwGfAh6VNDeNTQHOA2ZIOgV4BjgBICLmS5oBPEZy5ufpEbE2x/zMrCTaJ9/CVU8+D8DEybes1zYWn3d0PVOyJsmt6EXE76l+nA7g0D7WmQpMzSsnMzMrN9+RxczMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSiPPe2+amW2Q9vW8T6ZZX9zTMzOz0nDRMzOz0nDRMzOz0nDRMzOz0sjzyemXSVouaV5F7GpJc9PX4p6Hy0pql/RKxWeX5JWXmZmVV55nb04HLgR+2hOIiI/1TEv6PvCXiuX/FBFjcszHzMxKLs8np8+W1F7tM0kCTgQ+lNf+zczMemvWMb0PAMsi4omK2C6SHpJ0l6QPNCkvMzMrsGZdnH4ScGXF/FJgZEQ8L+kA4AZJe0XEit4rSpoETAIYOXJkQ5I1M7NiaHhPT9LGwEeBq3tiEbE6Ip5Ppx8A/gS8q9r6ETEtIjoioqOtra0RKZuZWUE0Y3jzMGBhRHT1BCS1SRqSTu8KjAKebEJuZmZWYHlesnAlcA+wu6QuSaekH03kzUObAAcDj0h6GLgWOC0iXsgrNzMzK6c8z948qY/4Z6rErgOuyysXMzMz8B1ZzMysRFz0zMysNFz0zMysNFz0zMysNFz0zMysNFz0zMysNFz0zMysNFz0zMysNFz0zMysNFz0zMysNFz0zMysNFz0zMysNFz0zMysNFz0zMysNFz0zMysNPJ8iOxlkpZLmlcRO1fSnyXNTV9HVXx2tqRFkh6XdHheeZmZWXnl2dObDhxRJX5BRIxJX7cCSBpN8kT1vdJ1LpI0JMfczMyshHIrehExG3gh4+LjgasiYnVEPAUsAsbmlZuZmZVTM47pnSHpkXT4c9s0NgJ4tmKZrjS2DkmTJHVK6uzu7s47VzMzK5BGF72Lgd2AMcBS4PtpXFWWjWobiIhpEdERER1tbW25JGlmZsW0cSN3FhHLeqYlXQrcnM52ATtXLLoTsKSBqZmZ9at98i112c7i846uy3Zs/TS0pydpeMXsBKDnzM6bgImSNpW0CzAKmNPI3MzMrPhy6+lJuhIYBwyT1AV8ExgnaQzJ0OVi4PMAETFf0gzgMWANcHpErM0rNzMzK6fcil5EnFQl/JN+lp8KTM0rHzMzM9+RxczMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSqOhjxYys3Ko12N4zOrNPT0zMysNFz0zMysNFz0zMyuNTEVP0t4D3bCkyyQtlzSvIvb/S1oo6RFJ10vaJo23S3pF0tz0dclA92dmZlZL1p7eJZLmSPpiT6HKYDpwRK/YTGDviNgH+CNwdsVnf4qIMenrtIz7MDMzyyxT0YuI9wOfAHYGOiVdIenDNdaZDbzQK3Z7RKxJZ+8Fdhp4ymZmZusn8zG9iHgC+AbwdeCDwP9Ohyo/up77/hzw64r5XSQ9JOkuSR/oayVJkyR1Surs7u5ez12bmVkZZT2mt4+kC4AFwIeAYyNiz3T6goHuVNK/AmuAX6ShpcDIiNgP+BfgCklbV1s3IqZFREdEdLS1tQ1012ZmVmJZL06/ELgUmBIRr/QEI2KJpG8MZIeSTgaOAQ6NiEi3sxpYnU4/IOlPwLuAzoFs28zMrD9Zi95RwCsRsRZA0kbAZhHx14j4WdadSTqCdHg0Iv5aEW8DXoiItZJ2BUYBT2bdrpmZWRZZj+ndAWxeMT80jfVJ0pXAPcDukroknULSY9wKmNnr0oSDgUckPQxcC5wWES9U3bCZmdl6ytrT2ywiVvXMRMQqSUP7WyEiTqoS/kkfy14HXJcxFzMzs/WStaf3sqT9e2YkHQC80s/yZmZmg07Wnt5ZwDWSlqTzw4GP5ZKRmZlZTjIVvYi4X9IewO6AgIUR8VqumZmZmdXZQJ6ndyDQnq6znyQi4qe5ZGVmZpaDTEVP0s+A3YC5wNo0HICLnpmZtYysPb0OYHTPxeRmZmatKOvZm/OAt+eZiJmZWd6y9vSGAY9JmkN6uzCAiPhILlmZmZnlIGvROzfPJMzMzBoh6yULd0l6BzAqIu5I78YyJN/UzMzM6ivro4VOJbkn5o/S0AjghpxyMjMzy0XWE1lOBw4CVsDfHyi7fV5JmZmZ5SFr0VsdEa/2zEjamOQ6PTMzs5aRtejdJWkKsLmkDwPXAL/KLy0zM7P6y1r0JgPdwKPA54FbgQE9Md3MzKzZMhW9iHg9Ii6NiBMi4vh0ut/hTUmXSVouaV5FbDtJMyU9kb5vW/HZ2ZIWSXpc0uHr3yQzM7Pqsp69+ZSkJ3u/aqw2HTiiV2wyMCsiRgGz0nkkjQYmAnul61wkyZdEmJlZXQ3k3ps9NgNOALbrb4WImC2pvVd4PDAunb4cuBP4ehq/KiJWA09JWgSMBe7JmJ+ZmVlNWYc3n694/TkifgB8aD32t0NELE23uZQ3LnsYATxbsVxXGluHpEmSOiV1dnd3r0cKZmZWVlkfLbR/xexGJD2/reqYh6rEqh4zjIhpwDSAjo4OXzZhZmaZZR3e/H7F9BpgMXDieuxvmaThEbFU0nBgeRrvAnauWG4nYMl6bN/MzKxPWe+9eUid9ncTcDJwXvp+Y0X8CknnAzsCo4A5ddqnmZkZkH1481/6+zwizq+yzpUkJ60Mk9QFfJOk2M2QdArwDMkJMUTEfEkzgMdIepKnR8Ta3ts0M2t17ZNvqct2Fp93dF22UzYDOXvzQJIeGcCxwGzefPLJm0TESX18dGgfy08FpmbMx8zMbMAG8hDZ/SNiJYCkc4FrIuKf8krMzMys3rLehmwk8GrF/KtAe92zMTMzy1HWnt7PgDmSrie5lGAC8NPcsjIzM8tB1rM3p0r6NfCBNPTZiHgov7TMzMzqL+vwJsBQYEVE/BDokrRLTjmZmZnlIusNp79Jco/Ms9PQJsDP80rKzMwsD1l7ehOAjwAvA0TEEup7GzIzM7PcZS16r6bPzwsASVvkl5KZmVk+sp69OUPSj4BtJJ0KfA64NL+0zKwZ6nW3ELPBqmbRkyTgamAPYAWwO3BORMzMOTczM7O6qln0IiIk3RARBwAudGZm1rKyHtO7V9KBuWZiZmaWs6zH9A4BTpO0mOQMTpF0AvfJKzEzM7N667foSRoZEc8ARzYoHzMzs9zU6undQPJ0haclXRcR/7ihO5S0O8mJMT12Bc4BtgFOBbrT+JSIuHVD92dmZtajVtFTxfSu9dhhRDwOjAGQNAT4M3A98Fnggoj4Xj32Y2Zm1lutE1mij+l6ORT4U0Q8ncO2zczM3qRW0dtX0gpJK4F90ukVklZKWlGH/U8ErqyYP0PSI5Iuk7RtHbZvZmb2d/0WvYgYEhFbR8RWEbFxOt0zv/WG7FjSW0ju53lNGroY2I1k6HMp8P0+1pskqVNSZ3d3d7VFzMzMqhrIo4Xq7UjgwYhYBhARyyJibUS8TnKLs7HVVoqIaRHREREdbW1tDUzXzMxaXTOL3klUDG1KGl7x2QRgXsMzMjOzQst6cXpdSRoKfBj4fEX4PySNITlhZnGvz8zMzDZYU4peRPwVeFuv2KeakYuZmZVHM4c3zczMGspFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSsNFz8zMSqNZD5FdDKwE1gJrIqJD0nbA1UA7yUNkT4yIF5uRn5mZFVMze3qHRMSYiOhI5ycDsyJiFDArnTczM6ubwTS8OR64PJ2+HDiueamYmVkRNavoBXC7pAckTUpjO0TEUoD0ffsm5WZmZgXVlGN6wEERsUTS9sBMSQuzrpgWyUkAI0eOzCs/M7NBrX3yLXXZzuLzjq7LdlpFU3p6EbEkfV8OXA+MBZZJGg6Qvi/vY91pEdERER1tbW2NStnMzAqg4T09SVsAG0XEynT6H4B/B24CTgbOS99vbHRuZq2sXn/5mxVZM4Y3dwCul9Sz/ysi4jZJ9wMzJJ0CPAOc0ITczMyswBpe9CLiSWDfKvHngUMbnY+ZmZXHYLpkwczMLFcuemZmVhouemZmVhouemZmVhouemZmVhouemZmVhouemZmVhouemZmVhouemZmVhouemZmVhouemZmVhouemZmVhouemZmVhouemZmVhouemZmVhrNeHL6zsBPgbcDrwPTIuKHks4FTgW600WnRMStjc7PzKxM2iffssHbWHze0XXIpDGa8eT0NcBXIuJBSVsBD0iamX52QUR8rwk5mZlZCTTjyelLgaXp9EpJC4ARjc7DzMzKp6nH9CS1A/sB96WhMyQ9IukySds2LzMzMyuiphU9SVsC1wFnRcQK4GJgN2AMSU/w+32sN0lSp6TO7u7uaouYmZlV1ZSiJ2kTkoL3i4j4JUBELIuItRHxOnApMLbauhExLSI6IqKjra2tcUmbmVnLa3jRkyTgJ8CCiDi/Ij68YrEJwLxG52ZmZsXWjLM3DwI+BTwqaW4amwKcJGkMEMBi4PNNyM3MzAqsGWdv/h5QlY98TZ6ZmeXKd2QxM7PScNEzM7PScNEzM7PSaMaJLGZWoR73PjSzbNzTMzOz0nDRMzOz0nDRMzOz0nDRMzOz0nDRMzOz0nDRMzOz0nDRMzOz0nDRMzOz0nDRMzOz0nDRMzOz0vBtyMzWk28fZpao1/+FxecdXZft9GfQ9fQkHSHpcUmLJE1udj5mZlYcg6roSRoC/B/gSGA0ydPURzc3KzMzK4pBVfSAscCiiHgyIl4FrgLGNzknMzMriMF2TG8E8GzFfBfw7iblYgXlY3Fm5TXYip6qxOJNC0iTgEnp7CpJj+ee1RuGAc81cH/NUpZ2QnnaWvp2vrdn4rvHNCyZnBXuO9V3q4bXp53v6OuDwVb0uoCdK+Z3ApZULhAR04BpjUyqh6TOiOhoxr4bqSzthPK01e0snrK0td7tHGzH9O4HRknaRdJbgInATU3OyczMCmJQ9fQiYo2kM4DfAEOAyyJifpPTMjOzghhURQ8gIm4Fbm12Hn1oyrBqE5SlnVCetrqdxVOWtta1nYqI2kuZmZkVwGA7pmdmZpYbF70qJH1J0jxJ8yWdVeXzT0h6JH39QdK+TUhzg2Vo5/i0jXMldUp6fxPS3GC12lmx3IGS1ko6voHp1VWG73ScpL+k3+lcSec0Ic0NluU7Tds6N13mrganWBcZvs//WfFdzkv//W7XhFQ3WIa2vlXSryQ9nC7z2fXaUUT4VfEC9gbmAUNJjnneAYzqtcz7gG3T6SOB+5qdd07t3JI3hsD3ARY2O+882pkuNwT4Lcnx5OObnXeO3+k44OZm59qAdm4DPAaMTOe3b3beebSz1/LHAr9tdt45fqdTgO+m023AC8BbBrov9/TWtSdwb0T8NSLWAHcBEyoXiIg/RMSL6ey9JNcTtpos7VwV6b8wYAt63SigRdRsZ+pM4DpgeSOTq7OsbW11Wdr5ceCXEfEMQES04vc60O/zJODKhmRWf1naGsBWkkTyB/kLwJqB7shFb13zgIMlvU3SUOAo3nzBfG+nAL9uSGb1lamdkiZIWgjcAnyuwTnWQ812ShpB8h/skibkV09Z/+2+Nx0i+rWkvRqbYl1kaee7gG0l3SnpAUmfbniWGy7z76L08yNI/nBrRVnaeiFJcVwCPAp8KSJeH+iOBt0lC80WEQskfReYCawCHqaPvyYkHUJS9FruWFfWdkbE9cD1kg4Gvg0c1tBEN1DGdv4A+HpErE3+iGxNGdv6IPCOiFgl6SjgBmBUQxPdQBnbuTFwAHAosDlwj6R7I+KPDU12AwzkdxHJ0ObdEfFCo/Krp4xtPRyYC3wI2A2YKel3EbFiIPtyT6+KiPhJROwfEQeTdKGf6L2MpH2AHwPjI+L5RudYD1naWbHsbGA3ScMalmCdZGhnB3CVpMXA8cBFko5rbJb1UautEbEiIlal07cCmxT0O+0CbouIlyPiOWA20HInnA3g/+hEWndoE8jU1s+SDFlHRCwCngL2WJ8d+bXuQdXt0/eRwELSk1YqPh8JLALe1+xcc27nO3njRJb9gT/3zLfSq1Y7ey07nRY9kSXjd/r2iu90LPBMEb9TkmGwWSQ9vqEkw2d7Nzvvercz/eytJEVii2bnm/N3ejFwbjq9Q/r7aNhA9+Phzequk/Q24DXg9Ih4UdJpABFxCXAO8DaSHgHAmmjNG7/Wauc/Ap+W9BrwCvCxSP/FtZha7SySWm09HviCpDUk3+nEIn6nkQyX3QY8ArwO/Dgi5jUx3/WV5d/uBOD2iHi5WUnWSa22fhuYLulRkifyfD2SXvyA+I4sZmZWGj6mZ2ZmpeGiZ2ZmpeGiZ2ZmpeGiZ2ZmpeGiZ2ZmpeGiZzbIpLfOOrxX7CxJF/WzfCteMmPWcC56ZoPPlSR32KjU8nfcMBsMXPTMBp9rgWMkbQogqR3YEfh4+lzD+ZK+VW1FSasqpo+XND2dbpN0naT709dBubfCbBBy0TMbZCK5l+sckrvmQ9LLuxr41/TOP/sAH0zv/5rVD4ELIuJAkjvt/LiOKZu1DN+GzGxw6hnivDF9/xxwoqRJJP9vhwOjSW6zlcVhwOiKp0hsLWmriFhZ16zNBjkXPbPB6QbgfEn7kzwa50Xgq8CB6T0JpwObVVmv8r6ClZ9vBLw3Il7JJ12z1uDhTbNBKJLH/9wJXEbS69saeBn4i6QdgCP7WHWZpD0lbcSbnzx9O3BGz4ykMTmkbTboueiZDV5XkjwD7qqIeBh4CJhPUgjv7mOdycDNwG+BpRXxfwY6JD0i6THgtNyyNhvE/JQFMzMrDff0zMysNFz0zMysNFz0zMysNFz0zMysNFz0zMysNFz0zMysNFz0zMysNFz0zMysNP4fTMiSxI8zTUMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 504x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## T-Test on Bootstrapped Std and Bootstrapped Turbo Mean \n",
    "\n",
    "# Applying the t-test\n",
    "Aspiration_type_2 = t_test(std_bootstrap_mean, turbo_bootstrap_mean, alpha = 0.05)\n",
    "print(Aspiration_type_2)\n",
    "\n",
    "# Plotting results in a histogram \n",
    "plot_t(std_bootstrap_mean, turbo_bootstrap_mean, Aspiration_type_2, cols=[\"Std\", \"Turbo\"]) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Analysis of the Bootstrapping T-Test (Aspiration) \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For Aspiration type, the t-test conducted on the bootstrapped std and turbo groups showed a small p-value of 0.0000, a small difference in means, a large degrees of freedom, and a CI that did not contain 0. From this we can reject the null hypothesis and there is a good chance that the difference in price means between the groups is not from random fluctuation/chance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-------- Bayesian Method - Aspiration = std: ----------- \n",
      "Mean = 9.278, Standard deviation = 0.497\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f7f30dd6a00>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Bayesian Method on Aspiration Column \n",
    "\n",
    "## Creating a Prior, Likelihood, and Posterior Distribution of Aspiration = std (Mean)\n",
    "\n",
    "print(\"-------- Bayesian Method - Aspiration = std: ----------- \")\n",
    "N = 10000 \n",
    "p = np.linspace(8, 11, num=N) \n",
    "\n",
    "num_samples = 150 # number of samples from sample dataset \n",
    "std_samples = std.sample(n=num_samples) # sampling dataset without replacement \n",
    "\n",
    "pp_price = ss.norm.pdf(p, loc=std_samples.mean(), \n",
    "                          scale=std_samples.std())\n",
    "\n",
    "pp_price = pp_price / pp_price.sum() # normalizing price \n",
    "\n",
    "like_price = comp_like(p, std_samples)\n",
    "post_price_std = posterior(pp_price, like_price)\n",
    "\n",
    "pyplot.plot(p, pp_price, label='prior')\n",
    "pyplot.plot(p, like_price, label='likelihood', alpha=.3, linewidth=10)\n",
    "pyplot.plot(p, post_price_std, label='posterior')\n",
    "pyplot.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-------- Bayesian Method - Aspiration = turbo: ----------- \n",
      "Mean = 9.612, Standard deviation = 0.390\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f7f3077fbe0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Creating a Prior, Likelihood, and Posterior Distribution of Aspiration = Turbo (Mean)\n",
    "\n",
    "print(\"-------- Bayesian Method - Aspiration = turbo: ----------- \")\n",
    "\n",
    "N = 10000 \n",
    "p = np.linspace(8, 11, num=N) \n",
    "\n",
    "num_samples = 30 # number of samples from sample dataset \n",
    "turbo_samples = turbo.sample(n=num_samples) # sampling dataset without replacement \n",
    "\n",
    "pp_price = ss.norm.pdf(p, loc=turbo_samples.mean(), \n",
    "                          scale=turbo_samples.std())\n",
    "\n",
    "pp_price = pp_price / pp_price.sum() # normalizing price \n",
    "\n",
    "like_price = comp_like(p, turbo_samples)\n",
    "post_price_turbo = posterior(pp_price, like_price)\n",
    "\n",
    "pyplot.plot(p, pp_price, label='prior')\n",
    "pyplot.plot(p, like_price, label='likelihood', alpha=.3, linewidth=10)\n",
    "pyplot.plot(p, post_price_turbo, label='posterior')\n",
    "pyplot.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DegFreedom    1.849408e+04\n",
      "Difference   -1.219727e-19\n",
      "Statistic    -2.190236e-14\n",
      "PValue        1.000000e+00\n",
      "Low95CI      -1.091562e-05\n",
      "High95CI      1.091562e-05\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "## T-Test on Bayesian Aspiration (Std & turbo) Mean\n",
    "\n",
    "# Applying the t-test\n",
    "Aspiration_type_3 = t_test(post_price_std, post_price_turbo, alpha = 0.05)\n",
    "print(Aspiration_type_3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------- CI for Standard Aspiration Prices: ----------\n",
      "The 0.950 credible interval is 0.025 to 0.975 \n",
      "\n",
      "The confidence interval for Bayesian method is from \n",
      " 9.198619861986199  to  9.357635763576358\n"
     ]
    },
    {
     "data": {
      "image/png": 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u6Uzvnr79tZk5qJjVbHhkmC0DW5jWPY3pk1JQedVBxQwcVMxqtmVgCwDTJ7mlYlbKQcWsRoUAMq17GlO6piDklopZ4qBiVqPN27IZrad1T6NNbUzrnrZ9mVmrc1Axq1EhgBS6vqZPmu7uL7PEQcWsRoWurmnd04AsuDiomGUcVMxqtL2lMqmopeIxFTPAQcWsZsVjKuCWilkxBxWzGhWf/QUwtWvq9tOMzVqdg4pZjTZv24wQU7umAllQ2TrguxSbgYOKWc02b9vM1K6ptCn7+kzpnOKWilnioGJWo60DW7e3UgCmdE3xfCpmiYOKWY36h/rp6ezZ/npK5xSGRoYYGB6YwFKZNQcHFbMa9Q32Mblz8vbXhVaLx1XMHFTMatY/1E9PR1FLpWsKgMdVzHBQMatZaUtlSmcWVDyuYtbgoCJpgaRVklZLuqjMekm6LK1/UNLR1fJK+htJj6b0N0qakZbPltQv6YH0WNLIulnr6h8sGVNJLRV3f5k1MKhIagcuBxYCc4EzJc0tSbYQmJMe5wFX5Mh7G3BERBwJPAZ8rmh7T0TEvPRY3JiaWavrG+zbqfurMKbi7i+zxrZUjgFWR8SaiBgArgUWlaRZBFwdmeXADEn7VcobEbdGxFDKvxw4oIF1MNtF/1C/u7/MRtHIoDILWFv0el1alidNnrwA/wn4SdHrQyT9WtKdkk4oVyhJ50laIWnFpk2b8tXErEj/YPmBend/mTU2qKjMssiZpmpeSV8AhoDvpkUbgIMi4veAzwDfkzRtl41EXBkR8yNifm9vb5UqmO3KA/Vmo+to4LbXAQcWvT4AWJ8zTVelvJLOBt4LnBwRARAR24Bt6fn9kp4A3gysqEdlzAp2ufjRpxSbbdfIlsp9wBxJh0jqAs4AlpakWQqclc4COw54OSI2VMoraQHwWeD9EdFX2JCk3jTAj6Q3kg3+r2lg/awFDY8MMzA8UHag3t1fZg1sqUTEkKQLgFuAduCbEbFS0uK0fgmwDDgVWA30AedWyps2/TWgG7hNEsDydKbXicCXJQ0Bw8DiiHixUfWz1tQ/1A+wU/dXT0cPQu7+MqOx3V9ExDKywFG8bEnR8wDOz5s3LT90lPQ3ADeMp7xm1fQNZo3j4u4vSUzunOzuLzN8Rb1ZTfoHd22pQDauUgg4Zq3MQcWsBoXur+IxlcLrwjqzVuagYlaDQmuktKXS09njlooZDipmNSl0fxWPqUAWZArrzFqZg4pZDbYP1Lv7y6wsBxWzGpQ7pRjc/WVW4KBiVgN3f5lV5qBiVoNRB+rd/WUGOKiY1WTUU4o7e9xSMcNBxawmlVoqHlMxc1Axq0nFMRV3f5k5qJjVom+wj462Djradr5tXk9H1v2VZmIwa1kOKmY1KJ1KuKCns4cgGBgemIBSmTUPBxWzGpROJVxQCDQeV7FW56BiVoO+ob7yLZUUaDyuYq3OQcWsBv2D/bsM0sOOgXufVmytzkHFrAZ9g5VbKu7+slbnoGJWg/6hymMq7v6yVuegYlaDvsE+d3+ZVeCgYlaD/sFRTin2QL0Z4KBiVpPRur8KLRWPqVirc1Axq8FoA/Xbx1Tc/WUtzkHFrAajXfzo7i+zjIOKWQ2qDdS7+8taXUODiqQFklZJWi3pojLrJemytP5BSUdXyyvpbyQ9mtLfKGlG0brPpfSrJJ3SyLpZ6xmJEbYNb3P3l1kFDQsqktqBy4GFwFzgTElzS5ItBOakx3nAFTny3gYcERFHAo8Bn0t55gJnAIcDC4Cvp+2Y1cWrQ68Cu07QBTCpYxLg7i+zRrZUjgFWR8SaiBgArgUWlaRZBFwdmeXADEn7VcobEbdGxFDKvxw4oGhb10bEtoh4ElidtmNWF6NN0AXQpja627vdUrGW18igMgtYW/R6XVqWJ02evAD/CfhJDftD0nmSVkhasWnTphzVMMuMNkFXQU+nZ380a2RQUZllpTMYjZamal5JXwCGgO/WsD8i4sqImB8R83t7e8tkMSuvUkulsNzdX9bqOqonGbN1wIFFrw8A1udM01Upr6SzgfcCJ8eOqfby7M9szAoBo9yYSmG5g4q1uka2VO4D5kg6RFIX2SD60pI0S4Gz0llgxwEvR8SGSnklLQA+C7w/IvpKtnWGpG5Jh5AN/t/bwPpZiym0VCp1f3lMxVpdw1oqETEk6QLgFqAd+GZErJS0OK1fAiwDTiUbVO8Dzq2UN236a0A3cJskgOURsTht+3rgt2TdYudHxHCj6metpxAwKnV/eUzFWl0ju7+IiGVkgaN42ZKi5wGcnzdvWn5ohf1dAlwy1vKaVeLuL7PqfEW9WU7VBurd/WXmoGKWW9VTijt8SrGZg4pZTj6l2Kw6BxWznHKNqbj7y1qcg4pZTrlOKXZLxVqcg4pZTv2D/bSrnc62zrLrPaZi5qBillv/UD89nT2k66N2MblzMgPDAwyP+PIoa10OKmY5jTaVcEGhW6xwi3yzVuSgYpZT/1D5qYQLPKWwmYOKWW55WyoeV7FW5qBillP/YP+oZ36BpxQ2AwcVs9z6Bvvc/WVWhYOKWU79Q/3u/jKrIldQkXSDpPdIchCyluXuL7Pq8gaJK4CPAo9LulTSWxtYJrOmVHWg3t1fZvmCSkTcHhEfA44GniKbIOsXks6VVP7yYrM9TNVTilMrxi0Va2W5u7Mk7Q2cA/wJ8GvgH8iCzG0NKZlZk8k7UO8xFWtluWZ+lPRD4K3At4H3pXnkAa6TtKJRhTNrJv2DlQfqt4+puPvLWlje6YT/MU3vu52k7ojYFhHzG1Aus6YSEdvv/TUad3+Z5e/++ssyy35Zz4KYNbPC/bw8UG9WWcWWiqQ3ALOAHkm/BxRuzzoNGP3bZbaHqTZBF0BXexdCHlOxllat++sUssH5A4C/K1r+CvD5BpXJrOlUm0oYQFI2pbC7v6yFVQwqEXEVcJWkD0XEDa9RmcyaTiFQVBpTKax395e1smrdXx+PiO8AsyV9pnR9RPxdmWxme5ztUwlX6P4qrHdQsVZWrftrSvo7tdEFMWtmhUBRqfsLspaKx1SslVXr/vpG+vvnY9m4pAVkF0m2k52WfGnJeqX1pwJ9wDkR8atKeSWdDlwMHAYcExEr0vLZwCPAqrT55RGxeCzlNiuVt/vLYyrW6vLeUPKvJU2T1Cnpp5Kel/TxKnnagcuBhcBc4ExJc0uSLQTmpMd5ZPcYq5b3YeCDwM/L7PaJiJiXHg4oVjd5BurB3V9mea9TeXdEbAbeC6wD3gz8jyp5jgFWR8SaiBgArgUWlaRZBFwdmeXADEn7VcobEY9ExCrMXkN5TikGd3+Z5Q0qhZtGngpcExEv5sgzC1hb9HpdWpYnTZ685Rwi6deS7pR0QrkEks6TtELSik2bNuXYpFn+loq7v6zV5Q0q/yLpUWA+8FNJvcCrVfKozLLImSZP3lIbgIMi4veAzwDfkzRtl41EXBkR8yNifm9vb5VNmmVyn1Ls7i9rcXlvfX8R8DZgfkQMAlvZtSur1DrgwKLXBwDrc6bJk7e0jNsi4oX0/H7gCbJuOrNxy31KcWePWyrW0vLeUBKys61mSyrOc3WF9PcBcyQdAjwDnEE20VexpcAFkq4FjgVejogNkjblyLuT1Hp6MSKGJb2RbPB/Tf7qmY1u+5hKjpaKx1SsleW99f23gTcBDwDDaXFQIahExJCkC4BbyE4L/mZErJS0OK1fAiwjG6dZTXZK8bmV8qaynAZ8FegFfizpgYg4BTgR+LKkoVTGxTnHfsyq6hvso01tdLd3V0w3uXOyu7+speVtqcwH5kZEtXGNnaTb5S8rWbak6HkA5+fNm5bfCNxYZvkNgG8lYw1RmEslu7RqdD0d7v6y1pZ3oP5h4A2NLIhZM6s262NBT2cPwzHM4PDga1Aqs+aTt6UyE/itpHuBbYWFEfH+hpTKrMn0DfVVPZ0Ydp5SeHqjC2XWhPIGlYsbWQizZtc3mC+oFE8p7KBirShXUImIOyUdDMyJiNslTSYbQDdrCdXmpy/wlMLW6vLe++s/Az8AvpEWzQJualCZzJpO3paKpxS2Vpd3oP584B3AZoCIeBzYp1GFMms2fYN9Va9RgR0tFV+rYq0qb1DZlm7sCEC6ALKm04vNdmc1j6m4+8taVN6gcqekzwM9kv4I+D7wL40rlllz6R/KOabi7i9rcXmDykXAJuAh4JNkFyV+sVGFMms2fYN9TO7IP1Dv7i9rVXnP/hqRdBNwU0T4fvHWcvKOqbj7y1pdxZaKMhdLeh54FFglaZOkL702xTNrDj77yyyfat1fnyI76+sPImLviNiL7G7C75D06UYXzqwZDI8MMzA84OtUzHKoFlTOAs6MiCcLCyJiDfDxtM5sj1doddR6mxazVlQtqHRGxPOlC9O4SmeZ9GZ7nLxTCUNRS8XdX9aiqgWVgTGuM9tj5J31EaCjrYPOtk53f1nLqnb211GSNpdZLmBSA8pj1nQKASJPSwXSlMJuqViLqhhUIsI3jbSWV0v3F3hKYWtteS9+NGtZtQYVTylsrcxBxayKmlsqnZ5S2FqXg4pZFYVWR54r6iHNU++WirUoBxWzKsbSUvGYirUqBxWzKsY0puLuL2tRDipmVYzl7C93f1mrclAxq6LQ6shz8SO4+8taW0ODiqQFklZJWi3pojLrJemytP5BSUdXyyvpdEkrJY1Iml+yvc+l9KskndLIulnrKASISR35rvft6fDZX9a6GhZUJLUDlwMLgbnAmZLmliRbCMxJj/OAK3LkfRj4IPDzkv3NBc4ADgcWAF9P2zEbl8Jt7yXlSu/rVKyVNbKlcgywOiLWpPntrwUWlaRZBFwdmeXADEn7VcobEY9ExKoy+1sEXBsR29JdlVen7ZiNS965VAp8Rb21skYGlVnA2qLX69KyPGny5B3L/pB0nqQVklZs2uRJLK26vqG+3OMpAFO7pvLq0KsE0cBSmTWnRgaVcn0Fpd+y0dLkyTuW/RERV0bE/IiY39vbW2WTZrB1YCtTu6bmTl9IOzwy0qgimTWtXHPUj9E64MCi1wcA63Om6cqRdyz7M6vZloEtYwsqMUwHHtaz1tLIlsp9wBxJh0jqIhtEX1qSZilwVjoL7Djg5YjYkDNvqaXAGZK6JR1CNvh/bz0rZK1pzEFlZLhRRTJrWg1rqUTEkKQLgFuAduCbEbFS0uK0fgmwDDiVbFC9Dzi3Ul4ASacBXwV6gR9LeiAiTknbvh74LTAEnB8R/lbbuG0Z2MKsadWG9HYobqmYtZpGdn8REcvIAkfxsiVFzwM4P2/etPxG4MZR8lwCXDKOIpvtYuvgWMdUHFSs9fiKerMqtgxsYWpn/qAypWsK4JaKtSYHFbMqPKZilp+DilkFwfjO/jJrNQ4qZhWMxAgjMbK9SysPt1SslTmomFVQCAxuqZjl46BiVkEhMNQSVLrbu2lXu1sq1pIcVMwqGBlDUJHE1K6pbqlYS3JQMatgLN1fhfRuqVgrclAxq6DQ2pjSmX+gHrJrVUbcUrEW5KBiVsG4WioOKtaCHFTMKhjLQH0hvbu/rBU5qJhV4JaKWW0cVMwqcEvFrDYOKmYVFAJDLXPUA0ztdEvFWpODilkFwzFMT0cP7W21zeDoloq1KgcVswqGRoaYPml6zfkKYyrRgDKZNTMHFbMKhkaGmd5de1CZ1j2NiOyGlGatxEHFrIKxtlQKeYZGhupdJLOm5qBiVsHwyNCYWiozJs0AHFSs9TiomFUw5pZKt1sq1pocVMwqGOuYSqGlMuygYi3GQcWsgqEYW/eXx1SsVTmomI0iCEZGRsbU/eUxFWtVDipmoxhKFy+OqaXiMRVrUQ0NKpIWSFolabWki8qsl6TL0voHJR1dLa+kvSTdJunx9Pf1aflsSf2SHkiPJY2sm+35CgFhLC2VyZ2TkXYEJrNW0bCgIqkduBxYCMwFzpQ0tyTZQmBOepwHXJEj70XATyNiDvDT9LrgiYiYlx6LG1MzaxWFQfaxtFQk0dHW4ZaKtZxGtlSOAVZHxJqIGACuBRaVpFkEXB2Z5cAMSftVybsIuCo9vwr4QAPrYC1sPC0VIAsq4aBiraWRQWUWsLbo9bq0LE+aSnn3jYgNAOnvPkXpDpH0a0l3Sjph/FWwVjaeMRWA9rYOn1JsLaejgdtWmWWl99cbLU2evKU2AAdFxAuSfh+4SdLhEbF5px1K55F1tXHQQQdV2aS1skJLZVr3tDHl75C7v6z1NLKlsg44sOj1AcD6nGkq5X0udZGR/m4EiIhtEfFCen4/8ATw5tJCRcSVETE/Iub39vaOsWrWCoZGBgGYOXnmmPJ7TMVaUSODyn3AHEmHSOoCzgCWlqRZCpyVzgI7Dng5dWlVyrsUODs9Pxv4EYCk3jTAj6Q3kg3+r2lc9WxPNzgyCBrnmIqDirWYhnV/RcSQpAuAW4B24JsRsVLS4rR+CbAMOBVYDfQB51bKmzZ9KXC9pD8GngZOT8tPBL4saQgYBhZHxIuNqp/t+QaHB+ls66BNY/vt1dneweCwg4q1lkaOqRARy8gCR/GyJUXPAzg/b960/AXg5DLLbwBuGGeRzbYbHBmks61zzPk72zoZiRG2DmxlSteUOpbMrHn5inqzUQwOD9HZPo6g0t4FwKa+TfUqklnTc1AxG8XgyCAd42ypAGza6qBircNBxWwU4+7+Sq2c5/uer1eRzJqeg4pZGRHB0PDguLq/ulJed39ZK3FQMSujb7CPkQg628Z+Lou7v6wVOaiYlbFx60Zgx2D7WLS3dSDJLRVrKQ4qZmWsfyW7gUP3OIKKyMZV3FKxVuKgYlbGhi0bAOgaR1AB6GrrdEvFWoqDilkZhZZKV3v3uLbT1d61PUCZtQIHFbMyNryyAYlxnf0F0N3RzdqX11ZPaLaHcFAxK2P9lvV0tXeXnYOhFt3tk3hu63NsG9pWl3KZNTsHFbMyNryyYVyD9AXdHVn32TOvPDPubZntDhxUzMpYu3ktXR3jG08BmJS24S4waxUOKmYlRmKEJ3/3JD0dPePeVnca6F+3ed24t2W2O3BQMSux/pX1bBveRk/HpHFvq9D99fTLT497W2a7AwcVsxJPvPgEAJPq0FJpVzv7Td2Px158bNzbMtsdOKiYlVjzu2wW6p7O8bdUAA7rPYxHNj1Sl22ZNTsHFbMSjz7/KF3tXXS31ymozDyMR55/hGyiU7M9m4OKWYkHnnuAub1zadN4r1LJvHXmW9m8bTPPbnm2Ltsza2YOKmYlfvPsbzhq36Pqtr3Dew/Ptvvcb+q2TbNm5aBiVmT9K+t5butzzHvDvLpt8w9m/QFtauOXa39Zt22aNSsHFbMidzx1BwAnHHRC3bY5tWsqR+17FPesvadu2zRrVg4qZkV+9uTPmDFpRl1bKgDHH3Q8v1j7C/oG++q6XbNm46BilgwMD3DTozdxyptOob2tva7bPu2tp9E/1M+yx5fVdbtmzcZBxSz54SM/5IX+F/jEkZ+o+7ZPPPhE9pu6H9+4/xt137ZZM2loUJG0QNIqSaslXVRmvSRdltY/KOnoankl7SXpNkmPp7+vL1r3uZR+laRTGlk327Ns3raZL/7sixzeezgLDl1Q9+23t7Vz4dsu5PY1t3PzYzfXfftmzaJhQUVSO3A5sBCYC5wpaW5JsoXAnPQ4D7giR96LgJ9GxBzgp+k1af0ZwOHAAuDraTtmoxoYHuDup+/mlO+cwlMvPcXlp15e966vgvOPOZ95b5jHmTecyZX3X8nv+n/XkP2YTaSOBm77GGB1RKwBkHQtsAj4bVGaRcDVkV1qvFzSDEn7AbMr5F0EnJTyXwXcAXw2Lb82IrYBT0pancpQ9/M4H3ruIT7yg49sfx3sfKV0uSunq6VptvXNUIbXog59g30MjQwxY9IMrvvwdbxz9jt32Ua9TOqYxI8/+mNO//7pfPLmT/LJmz/JjEkzmN49nY62DtrUhiSEdvpr1ggLD13IV979lbpvt5FBZRZQPInEOuDYHGlmVcm7b0RsAIiIDZL2KdrW8jLb2omk88haRRx00EE1VGeHns4ejtjniNLt7vy6zJyB1dJM+Prdscxl/unWso3JnZM5ct8jec+b38PUrqm7bKve9n/d/tx97t3cs/Ye7n76bta/sp6XXn2J4RgmIhiJEYIgIsoGSbN6mfW6Xf491kUjg0q5n1il35LR0uTJO5b9ERFXAlcCzJ8/f0zf2kP3OpTrT79+LFnNkMTxBx3P8QcdP9FFMau7Rg7UrwMOLHp9ALA+Z5pKeZ9LXWSkvxtr2J+ZmTVQI4PKfcAcSYdI6iIbRF9akmYpcFY6C+w44OXUtVUp71Lg7PT8bOBHRcvPkNQt6RCywf97G1U5MzPbVcO6vyJiSNIFwC1AO/DNiFgpaXFavwRYBpwKrAb6gHMr5U2bvhS4XtIfA08Dp6c8KyVdTzaYPwScHxHDjaqfmZntqpFjKkTEMrLAUbxsSdHzAM7PmzctfwE4eZQ8lwCXjKPIZmY2Dr6i3szM6sZBxczM6sZBxczM6sZBxczM6kblbinSKiRtAv59HJuYCTxfp+JMpD2lHuC6NKM9pR7guhQcHBG95Va0dFAZL0krImL+RJdjvPaUeoDr0oz2lHqA65KHu7/MzKxuHFTMzKxuHFTG58qJLkCd7Cn1ANelGe0p9QDXpSqPqZiZWd24pWJmZnXjoGJmZnXjoFKFpE9LWinpYUnXSJpUsl6SLpO0WtKDko6eqLJWk6MuJ0l6WdID6fGliSprNZL+e6rHSkmfKrN+tzguOerRtMdE0jclbZT0cNGyvSTdJunx9Pf1o+RdIGlVOj4XvXalLm+cdXlK0kPp+Kx47Upd3ih1OT19xkYkjXoacV2OS0T4McqDbDriJ4Ge9Pp64JySNKcCPyGbefI44N8mutzjqMtJwM0TXdYcdTkCeBiYTHan7duBObvbcclZj6Y9JsCJwNHAw0XL/hq4KD2/CPirMvnagSeANwJdwG+AubtjXdK6p4CZE308qtTlMOAtwB3A/FHy1eW4uKVSXQfQI6mD7MtfOpvkIuDqyCwHZhRmpmxC1eqyuzgMWB4RfRExBNwJnFaSZnc4Lnnq0bQi4ufAiyWLFwFXpedXAR8ok/UYYHVErImIAeDalG/CjKMuTadcXSLikYhYVSVrXY6Lg0oFEfEM8BWyycA2kM1MeWtJslnA2qLX69KyppKzLgBvk/QbST+RdPhrWsj8HgZOlLS3pMlkrZIDS9LsDsclTz1g9zgmBftGNnsr6e8+ZdLsDscG8tUFIIBbJd0v6bzXrHT1V5fj4qBSQepDXQQcAuwPTJH08dJkZbI23XnaOevyK7J7+hwFfBW46TUtZE4R8QjwV8BtwL+SNdOHSpI1/XHJWY/d4pjUqOmPTY3eERFHAwuB8yWdONEFGqO6HBcHlcreBTwZEZsiYhD4IfD2kjTr2PnX5QE0Z7dS1bpExOaI2JKeLwM6Jc187YtaXUT8U0QcHREnkjX1Hy9Jslscl2r12J2OSfJcoZsx/d1YJs1ucWzIVxciYn36uxG4kawbaXdUl+PioFLZ08BxkiZLEtk0xo+UpFkKnJXONjqOrFtpw2td0Byq1kXSG9I6JB1D9vl44TUvaQ6S9kl/DwI+CFxTkmS3OC7V6rE7HZNkKXB2en428KMyae4D5kg6RFIXcEbK12yq1kXSFEmvKzwH3k3Wrbk7qs9xmegzFZr9Afw58CjZB+XbQDewGFic1gu4nOysiYcY5cyKZnjkqMsFwEqybpjlwNsnuswV6nIX8NtU1pPTst3uuOSoR9MeE7IAuAEYJPuV+8fA3sBPyVpcPwX2Smn3B5YV5T0VeCwdny/srnUhO1PqN+mxsonrclp6vg14DrilUcfFt2kxM7O6cfeXmZnVjYOKmZnVjYOKmZnVjYOKmZnVjYOKmZnVjYOKtSxJw+nOsg9L+n66VcpEl+kkSaUX2DZ6n7OL72hrNh4OKtbK+iNiXkQcAQyQXR9SVbohZ6OcxK53baioweUxq4mDilnmLuBQSe+T9G+Sfi3pdkn7Aki6WNKVkm4Frk6/7u+S9Kv0eHtKd5KkOyVdL+kxSZdK+pike9OcG29K6Xol3SDpvvR4h6TZZIHt06kFdUK5dOXKU1wRSddJOrXo9bckfWi0MpfkPUfS14pe3yzppPT83ZJ+mfJ+X9LUeh4A2zP4F461vPRLfyHZTR3vBo6LiJD0J8D/BC5MSX8fOD4i+lNX2R9FxKuS5pBdxVyY/OgostvavwisAf4xIo6R9N+B/wZ8CvgH4O8j4u50i5ZbIuIwSUuALRHxlVS275WmS9veqTwlVboW+AiwLN1u42Tgv5DdZWC0Mld7j2YCXwTeFRFbJX0W+Azw5Tz5rXU4qFgr65H0QHp+F/BPZBMZXZduINhFNrFZwdKif+CdwNckzQOGgTcXpbsv0n3GJD0BFKYYeAj4w/T8XcDcdFsvgGmFe0iVqJRuaZmAAtnkZJdJ6gYWAD9PgXB6hTJXcxwwF7gnlaUL+GUN+a1FOKhYK+uPiHnFCyR9Ffi7iFiaun0uLlq9tej5p8nuoXQUWTfyq0XrthU9Hyl6PcKO71wb8LbSoFAUPMiRbmtpYoDUErkDOIWsxVK4SWWlMhcMsXO3eGHKaQG3RcSZ5fZpVuAxFbOdTQeeSc/PrpJuQ0SMAJ8gm4q1FreS3SwSgNR6AHgFeF2OdNVcC5wLnEDWZZa3zE8B8yS1STqQHbdxXw68Q9KhqRyTJdXS0rEW4aBitrOLge9Lugt4vkK6rwNnS1pO1o1UttVQwZ8C8yU9KOm37Djz7F+A0woD9RXSVXMr2Vzlt0c2NWzeMt9D1uX3ENlMob8CiIhNwDnANZIeJAsyb62lwtYafJdiMzOrG7dUzMysbhxUzMysbhxUzMysbhxUzMysbhxUzMysbhxUzMysbhxUzMysbv4v6P24ZeUT8LgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plotting Posterior Distribution and CI of the mean of Standard Aspiration Prices \n",
    "print(\"---------- CI for Standard Aspiration Prices: ----------\")\n",
    "num_samples = 100000\n",
    "\n",
    "plot_ci(p, post_price_std, num_samples, lower_q=.025, upper_q=.975)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------- CI for Turbo Aspiration Prices: ----------\n",
      "The 0.950 credible interval is 0.025 to 0.975 \n",
      "\n",
      "The confidence interval for Bayesian method is from \n",
      " 9.474047404740475  to  9.747974797479749\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plotting Posterior Distribution and CI of the mean of Turbo Aspiration Prices \n",
    "print(\"---------- CI for Turbo Aspiration Prices: ----------\")\n",
    "\n",
    "plot_ci(p, post_price_turbo, num_samples, lower_q=.025, upper_q=.975)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Analysis of the Bayesian Method T-Test Results (Aspiration) \n",
    "For Aspiration type, the t-test conducted on the std and turbo groups after applying the Bayesian method showed a p-value of 1.0000, a small t-statistic, and a CI that does contain 0. This does not seem to support the findings of previous analysis, however, the CI plots between the standard aspiration vs turbo aspiration show that the CI do not overlap each other. We can say that with 95% certainty, the prices of standard aspiration and prices of turbo aspiration are significantly different from each other. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.) Compare the results from step 4 above with those you found in Assignment 04 with classical t-tests, Tukey HSD, and ANOVA."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When conducting the classic t-test on Aspiration types, the t-test conducted on the std and turbo groups showed a small p-value of 0.00004, a small difference in means, a large t-statistic, and a CI that did not contain 0. From this we rejected the null hypothesis (since p < alpha) and there is a good chance that the difference in price means between the groups is not from random fluctuation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multiple Comparison of Means - Tukey HSD, FWER=0.05\n",
      "=================================================\n",
      "group1 group2 meandiff p-adj lower  upper  reject\n",
      "-------------------------------------------------\n",
      "   std  turbo   0.3265 0.001 0.1537 0.4992   True\n",
      "-------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "## Calculating the Tukey HSD for Aspiration Categories: \n",
    "Tukey_HSD = pairwise_tukeyhsd(Auto.LogPrice, Auto.aspiration)\n",
    "print(Tukey_HSD)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above is a Tukey HSD analysis - which conducts a pairwise group analysis on the turbo and standard aspiration. We see that the upper and lower CI levels do not contain zero and that the groups are truly different from each other. We reject the null hypothesis that these two groups are the same. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F statistic = 13.877893412762756\n",
      "P-value = 0.0002528012774381665\n"
     ]
    }
   ],
   "source": [
    "## Calculating the F-statistic and p-value for ANOVA Analysis\n",
    "f_statistic, p_value = ss.f_oneway(std, turbo) \n",
    "\n",
    "print('F statistic = ' + str(f_statistic))\n",
    "print('P-value = ' + str(p_value))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above is the ANOVA analysis for aspiration groups. The F statistic is quite large and the p-value is small. Once again, we can reject the null hypothesis that the turbo and standard aspiration categories have the same price. The probability of the differences being due to random chance is low.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In summary, the classic t-test, ANOVA, Tukey HSD, bootstrapping and bayesian method analsis all point to the same findings - that the aspiration groups (standard and turbo) do have significantly different price groups. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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