{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# IntroStat Week 4 \n",
    "\n",
    "Welcome to the 4th lecture in IntroStat\n",
    "\n",
    "During the lectures we will present both slides and notebooks. \n",
    "\n",
    "This is the notebook used in the lecture in week 4.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation: Distribution of the sample mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot histogram of 10 random values (normally distributed)\n",
    "\n",
    "# 'True' values in theoretical population\n",
    "mu = 178\n",
    "sigma = 12\n",
    "\n",
    "# size of sample\n",
    "n = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[194.63824055 183.78584889 176.88110323 162.81659234 182.51879556\n",
      " 183.48484835 191.84214443 179.75311414 150.27557913 176.65952345\n",
      " 197.98279405 180.55317506 190.37244549 187.97008201 164.68632257\n",
      " 167.50045091 189.76482532 202.74971016 174.55433143 207.22052531\n",
      " 164.01151719 176.67450992 167.93948897 172.84076454 147.3351689\n",
      " 180.6324294  161.94555453 185.36003266 189.92539381 165.0060149 ]\n"
     ]
    }
   ],
   "source": [
    "# Draw 10 random numbers\n",
    "x = stats.norm.rvs(mu, sigma, size=n)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "182.49803934124503\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# calculate sample mean and plot\n",
    "x = stats.norm.rvs(mu, sigma, size=n)\n",
    "print(x.mean())\n",
    "\n",
    "# Plot histogram \n",
    "plt.hist(x, density=True)\n",
    "plt.xlim(140,220)\n",
    "plt.ylim(0,0.20)\n",
    "plt.axvline(x.mean(), linestyle='--', color=\"black\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[175.66169122 177.13254301 172.43781195 178.80790596 175.65865673\n",
      " 178.9695778  175.86839557 179.09752116 178.8575567  181.64402763\n",
      " 179.5666075  178.47810968 180.17923155 177.18045155 176.5796046\n",
      " 179.06196124 179.62128581 179.08622548 178.25604893 179.60406186\n",
      " 178.00735477 179.17757343 183.8779801  182.18692298 175.77747403\n",
      " 178.44927029 176.67924432 178.97093185 176.19733819 178.39083273\n",
      " 180.28771838 177.04097579 177.42246727 176.98030275 178.38528514\n",
      " 178.92196558 180.36500187 177.66964386 173.47894791 178.19173152\n",
      " 175.21184085 177.66416095 179.89389535 175.6254453  177.83870853\n",
      " 174.17681378 179.52531957 177.63802543 177.95256533 177.90253285\n",
      " 177.36474462 177.72883301 178.18402266 177.69613894 179.11164646\n",
      " 178.71620266 177.17435412 180.8888412  179.59553164 173.77398452\n",
      " 178.84112958 176.59891246 177.21300349 179.38093053 179.72442614\n",
      " 180.61877573 176.55149759 181.6891367  179.57109028 178.71693947\n",
      " 177.94987156 174.7336416  176.44805829 184.73661241 179.90740606\n",
      " 177.95130769 178.62416691 177.8324894  176.891367   177.84210044\n",
      " 176.7199597  178.77198157 178.25429476 178.22485357 176.53449769\n",
      " 178.00566398 182.55475937 180.8312307  177.79054151 180.63081277\n",
      " 179.18800281 178.50853278 179.43139975 182.5253572  175.77592938\n",
      " 177.9030209  176.52232348 177.51917374 177.21606941 178.58963766]\n"
     ]
    }
   ],
   "source": [
    "# Repeat 100 times and plot histogram of the mean values\n",
    "\n",
    "# Draw (10 x 100) random numbers\n",
    "mat = stats.norm.rvs(mu, sigma, size=(n,100))\n",
    "\n",
    "# Calculate sample mean of each column \n",
    "xbar = mat.mean(axis=0)\n",
    "\n",
    "print(xbar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot histogram of the mean values\n",
    "plt.hist(xbar, density=True, color=\"black\")\n",
    "plt.xlim(160,195)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### t-distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the t-distribution\n",
    "plt.plot(np.arange(-3,3,.01), stats.t.pdf(np.arange(-3,3,.01), df=9), color=\"red\")\n",
    "plt.show()\n",
    "\n",
    "#np.arange(start, stop, step): Creating 600 values between -3 and 3, which are x-axis limits\n",
    "#stats.t.pdf(np.arange(-3, 3, .01), df=9) calculates the probability density function (PDF) \n",
    "# of the t-distribution for each value in the array generated by np.arange(-3, 3, .01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: find correct quantile in t(9)-distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "height_data = np.array([168, 161, 167, 179, 184, 166, 198, 187, 191, 179])\n",
    "xrange = np.arange(140, 220, .1)\n",
    "plt.hist(height_data, density=True)\n",
    "plt.ylim(0,.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "178.0\n",
      "12.211106056009468\n"
     ]
    }
   ],
   "source": [
    "# calculate mean (xbar) and sample standard deviation (S)\n",
    "xbar = height_data.mean()\n",
    "s = height_data.std(ddof=1)\n",
    "print(xbar)\n",
    "print(s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Critical values of Student's t distribution with ν degrees of freedom\n",
    "\n",
    "When, $\\alpha = 0.1$, $90\\%$ confidence level<br>\n",
    "$\\alpha/2 = 0.05$\n",
    "$1-\\alpha/2 = 1-0.05=0.95$\n",
    "\n",
    "When, $\\alpha = 0.05$, $95\\%$ confidence level<br>\n",
    "$\\alpha/2 = 0.05/2=0.025$\n",
    "$1-\\alpha/2 = 1-0.025=0.975$\n",
    "\n",
    "When, $\\alpha = 0.01$, $99\\%$ confidence level<br>\n",
    "$\\alpha/2 = 0.01/2=0.005$\n",
    "$1-\\alpha/2 = 1-0.005=0.995$\n",
    "\n",
    "Typical or default confidence level is $\\alpha = 0.05$, $95\\%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For significance level 0.1 (df=9), The lower limit is -1.83 and the upper limit is 1.83\n",
      "For significance level 0.05 (df=9), The lower limit is -2.26 and the upper limit is 2.26\n",
      "For significance level 0.01 (df=9), The lower limit is -3.25 and the upper limit is 3.25\n"
     ]
    }
   ],
   "source": [
    "#For significance level 0.1 (df=9), critical values of Student's t distribution with 9 degrees of freedom\n",
    "t_lower = stats.t.ppf(q=0.05,df=9)\n",
    "t_upper = stats.t.ppf(q=0.95,df=9)\n",
    "print(\"For significance level 0.1 (df=9), The lower limit is \" + str(round(t_lower,2))\n",
    "      + \" and the upper limit is \" + str(round(t_upper,2)))\n",
    "\n",
    "#For significance level 0.05(df=9), critical values of Student's t distribution with 9 degrees of freedom\n",
    "t_lower = stats.t.ppf(q=0.025,df=9)\n",
    "t_upper = stats.t.ppf(q=0.975,df=9)\n",
    "print(\"For significance level 0.05 (df=9), The lower limit is \" \n",
    "      + str(round(t_lower,2))+ \" and the upper limit is \" + str(round(t_upper,2)))\n",
    "\n",
    "#For significance level 0.01(df=9), critical values of Student's t distribution with 9 degrees of freedom\n",
    "t_lower = stats.t.ppf(q=0.005,df=9)\n",
    "t_upper = stats.t.ppf(q=0.995,df=9)\n",
    "print(\"For significance level 0.01 (df=9), The lower limit is \" \n",
    "      + str(round(t_lower,2))+ \" and the upper limit is \" + str(round(t_upper,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $95\\%$ Interval Estimate for students' height sample data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[169.26, 186.74]\n"
     ]
    }
   ],
   "source": [
    "# 95% interval estimte for students' height sample data\n",
    "\n",
    "height_data = np.array([168, 161, 167, 179, 184, 166, 198, 187, 191, 179])\n",
    "xbar = height_data.mean()\n",
    "s = height_data.std(ddof=1)\n",
    "\n",
    "t_lower = stats.t.ppf(q=0.025,df=9)\n",
    "t_upper = stats.t.ppf(q=0.975,df=9)\n",
    "\n",
    "mu_lower = xbar + t_lower*s/np.sqrt(10)\n",
    "mu_upper = xbar + t_upper*s/np.sqrt(10)\n",
    "print([round(mu_lower,2), round(mu_upper,2)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualize the confidence interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the confidence interval\n",
    "xrange = np.arange(140, 220, .1)\n",
    "plt.hist(height_data, density=True)\n",
    "\n",
    "# Sample mean line\n",
    "plt.axvline(xbar, linestyle='-', color=\"blue\", ymin=0, ymax=1, label=\"Sample Mean\")\n",
    "\n",
    "# Confidence interval range\n",
    "plt.plot([xbar - s/np.sqrt(10), xbar + s/np.sqrt(10)], [0.1, 0.1], linestyle='-', color=\"blue\", label=\"Confidence Interval\")\n",
    "\n",
    "# Lower bound of confidence interval\n",
    "plt.axvline(mu_lower, linestyle='--', color=\"blue\", ymin=0, ymax=1, label=\"Lower CI Bound\")\n",
    "\n",
    "# Upper bound of confidence interval\n",
    "plt.axvline(mu_upper, linestyle='--', color=\"blue\", ymin=0, ymax=1, label=\"Upper CI Bound\")\n",
    "\n",
    "# Set axis limits and labels\n",
    "plt.ylim(0, .2)\n",
    "plt.xlabel(\"Height\")\n",
    "plt.ylabel(\"Density\")\n",
    "plt.title(\"Confidence Interval for Sample Mean\")\n",
    "\n",
    "# Add legend to label the lines\n",
    "plt.legend()\n",
    "\n",
    "# Show plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also calcualte a 99%-confidence interval for our mean student height\n",
    "\n",
    "Will it be wider or narrower ?\n",
    "\n",
    "Try to calculate the 99% interval using Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation: Distribution of the sample variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "124.59567239536841\n",
      "144\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run this multiple times and observe changes in the plot\n",
    "\n",
    "# Back to simulation of student heights\n",
    "mu = 178\n",
    "sigma = 12\n",
    "n = 10\n",
    "\n",
    "# calculate sample VARIANCE\n",
    "x = stats.norm.rvs(mu, sigma, size=n)\n",
    "print(x.var())\n",
    "print(sigma**2)\n",
    "\n",
    "# Plot histogram \n",
    "plt.hist(x, density=True)\n",
    "plt.xlim(150,220)\n",
    "plt.ylim(0,0.20)\n",
    "plt.axvline(x.mean(), linestyle='--', color=\"black\") #verticle line\n",
    "plt.plot([x.mean()-x.std(),x.mean()+x.std()], [.1, .1], '|', linestyle=\"-\", color='grey')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not only sample mean changes for each simulation - also the sample variance changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Repeat 100 times and plot histogram of the variance values\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "\n",
    "# Draw (10 x 100) random numbers\n",
    "mat = stats.norm.rvs(mu, sigma, size=(n,100))\n",
    "\n",
    "# Calculate sample mean of each column \n",
    "s2 = mat.var(axis=0)\n",
    "\n",
    "# Adding labels and title to the plot\n",
    "plt.title(\"Histogram of Sample Variance Values\")\n",
    "plt.xlabel(\"Variance Values\")\n",
    "plt.ylabel(\"Density\")\n",
    "\n",
    "plt.hist(s2, density=True, color=\"grey\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variance is always positive and does not follow a normal distribution. <br>\n",
    "The distribution of variance is not symmetrical. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Variance of student heights "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "149.11111111111111\n"
     ]
    }
   ],
   "source": [
    "# A random sample of n = 10 student height have the following sample mean and variance:\n",
    "height_data = np.array([168, 161, 167, 179, 184, 166, 198, 187, 191, 179])\n",
    "xbar = height_data.mean()\n",
    "s = height_data.std(ddof=1)\n",
    "n=10\n",
    "\n",
    "var_hat = s**2\n",
    "print(var_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot chi-square distribution with n-1 = 9 degrees of freedom\n",
    "plt.plot(np.arange(0,50,.1), stats.chi2.pdf(np.arange(0,50,.1), df=(n-1), loc=0, scale=1), color=\"red\")\n",
    "xint = np.arange(0, stats.chi2.ppf(0.025, df=(n-1), loc=0, scale=1), .01)\n",
    "plt.fill_between(xint, stats.chi2.pdf(xint, df=(n-1), loc=0, scale=1), color='red', alpha=0.3)\n",
    "xint = np.arange(stats.chi2.ppf(0.975, df=(n-1), loc=0, scale=1), 50, .01)\n",
    "plt.fill_between(xint, stats.chi2.pdf(xint, df=(n-1), loc=0, scale=1), color='red', alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.7004, 19.0228]\n"
     ]
    }
   ],
   "source": [
    "#chi2_lower = stats.chi2.ppf(0.025, df=(n-1), loc=0, scale=1)\n",
    "#chi2_upper = stats.chi2.ppf(0.975, df=(n-1), loc=0, scale=1)\n",
    "\n",
    "chi2_lower = stats.chi2.ppf(0.025, df=(n-1))\n",
    "chi2_upper = stats.chi2.ppf(0.975, df=(n-1))\n",
    "\n",
    "print([round(chi2_lower,4), round(chi2_upper,4)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Confidence interval for the variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "149.11111111111111\n",
      "70.5470420606106\n",
      "496.96534518807795\n"
     ]
    }
   ],
   "source": [
    "# confidence interval for the variance\n",
    "print(var_hat)\n",
    "print((n-1)*var_hat/chi2_upper) # lower limit of the interval\n",
    "print((n-1)*var_hat/chi2_lower) # upper limit of the interval"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Confidence interval for the standard deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard deviation: 12.211106056009468\n",
      "95% confidence interval for the standard deviation\n",
      "8.399228658669236\n",
      "22.29271955567732\n"
     ]
    }
   ],
   "source": [
    "# confidence interval for the standard deviation\n",
    "print(\"Standard deviation: \" + str(np.sqrt(var_hat))) # notice - square root\n",
    "print(\"95% confidence interval for the standard deviation\")\n",
    "print(np.sqrt((n-1)*var_hat/chi2_upper))\n",
    "print(np.sqrt((n-1)*var_hat/chi2_lower))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the interval is not symmetric"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CLT in action"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=1\n",
    "k=1000\n",
    "u = stats.uniform.rvs(loc=0, scale=30, size=(n,k))\n",
    "\n",
    "mean_values = u.mean(axis=0)\n",
    "\n",
    "plt.hist(mean_values, density=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now increase n to 2,3,6,30"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also try with another distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=30\n",
    "k=1000\n",
    "u = stats.expon.rvs(loc=0, scale=30, size=(n,k))\n",
    "mean_values = u.mean(axis=0)\n",
    "\n",
    "plt.hist(mean_values, density=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now increase n to 2,3,6,30"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Exam question from 2016 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "grades = np.array([2, 4, 7, 10, 12])\n",
    "count = np.array([22, 78, 84, 72, 24])\n",
    "#plt.bar(grades,count)\n",
    "#plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average grade: 6.97\n"
     ]
    }
   ],
   "source": [
    "# calculate average (mean) grade:\n",
    "total_grade = np.sum(grades*count)\n",
    "avg_grade = total_grade/280\n",
    "print(\"Average grade: \" + str(round(avg_grade,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The formula for sample variance ($ s^2 $) is:\n",
    "\n",
    "$s^2 = \\frac{1}{n-1} \\sum_{i=1}^{n} (x_i - \\bar{x})^2$\n",
    "\n",
    "Where:\n",
    "- $ n $ is the sample size.\n",
    "- $ x_i $ represents each individual observation.\n",
    "- $ \\bar{x} $ is the sample mean. \n",
    "  \n",
    "For this question, the frequncy or count has to be taken into consideration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.97142857, -2.97142857,  0.02857143,  3.02857143,  5.02857143])"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grades-avg_grade"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance of grade: \n",
      "8.96\n"
     ]
    }
   ],
   "source": [
    "# calculate variance of grades:\n",
    "\n",
    "var_grade = 1/(280-1)* np.sum(count * (grades-avg_grade)**2)\n",
    "print(\"Variance of grade: \")\n",
    "print(round(var_grade,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.17888298474012831\n"
     ]
    }
   ],
   "source": [
    "avg_grade_standard_error = np.sqrt(var_grade)/np.sqrt(280)\n",
    "print(avg_grade_standard_error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.968503126548004\n"
     ]
    }
   ],
   "source": [
    "t_upper = stats.t.ppf(0.975, df=280-1)\n",
    "print(t_upper)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.61929685668139\n",
      "7.323560286175753\n"
     ]
    }
   ],
   "source": [
    "print(avg_grade - t_upper*avg_grade_standard_error)\n",
    "print(avg_grade + t_upper*avg_grade_standard_error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Production of tablets "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.004900000000000001\n"
     ]
    }
   ],
   "source": [
    "# A random sample of n = 20 have the following sample mean and variance:\n",
    "\n",
    "n = 20\n",
    "mu_hat = 1.01\n",
    "var_hat = 0.07**2\n",
    "\n",
    "print(var_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to give a confidence interval on the estimate of var_hat\n",
    "\n",
    "We choose a 95% confidence interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot chi-square distribution and visualise the limits of chi^2\n",
    "\n",
    "# we need the distribution of n-1 = 19 degrees of freedom\n",
    "\n",
    "plt.plot(np.arange(0,50,.1), stats.chi2.pdf(np.arange(0,50,.1), df=(n-1), loc=0, scale=1), color=\"red\")\n",
    "xint = np.arange(0, stats.chi2.ppf(0.025, df=(n-1), loc=0, scale=1), .01)\n",
    "plt.fill_between(xint, stats.chi2.pdf(xint, df=(n-1), loc=0, scale=1), color='peachpuff', alpha=0.6)\n",
    "xint = np.arange(stats.chi2.ppf(0.975, df=(n-1), loc=0, scale=1), 50, .01)\n",
    "plt.fill_between(xint, stats.chi2.pdf(xint, df=(n-1), loc=0, scale=1), color='peachpuff', alpha=0.6)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[8.906516481987971, 32.85232686172969]\n"
     ]
    }
   ],
   "source": [
    "chi2_lower = stats.chi2.ppf(0.025, df=(n-1), loc=0, scale=1)\n",
    "chi2_upper = stats.chi2.ppf(0.975, df=(n-1), loc=0, scale=1)\n",
    "\n",
    "print([chi2_lower,chi2_upper])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.004900000000000001\n",
      "0.010453020570756269\n",
      "0.002833893635353239\n"
     ]
    }
   ],
   "source": [
    "# confidence interval for the variance\n",
    "print(var_hat)\n",
    "print((n-1)*var_hat/chi2_lower)\n",
    "print((n-1)*var_hat/chi2_upper)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variance\n",
    "A $ 100(1-\\alpha)\\% $ confidence interval for the variance $ \\sigma^2 $ is given by:\n",
    "\n",
    "$\n",
    "\\left[ \\frac{(n-1)s^2}{\\chi^2_{1-\\alpha/2}};~\n",
    "\\frac{(n-1)s^2}{\\chi^2_{\\alpha/2}} \\right],\n",
    "$\n",
    "\n",
    "where the quantiles come from a $ \\chi^2 $ distribution with $ n - 1 $ degrees of freedom.\n",
    "\n",
    "### Standard Deviation\n",
    "A $ 100(1-\\alpha)\\% $ confidence interval for the standard deviation $ \\sigma $ is:\n",
    "\n",
    "$\n",
    "\\left[ \\sqrt{\\frac{(n-1)s^2}{\\chi^2_{1-\\alpha/2}}};~\n",
    "\\sqrt{\\frac{(n-1)s^2}{\\chi^2_{\\alpha/2}}} \\right].\n",
    "$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.211106056009468\n",
      "Confidence Interval Estimates for the Variance of the active ingredient-concentration :\n",
      "15.08\n",
      "40.02\n"
     ]
    }
   ],
   "source": [
    "# confidence interval for the standard deviation\n",
    "print(np.sqrt(var_hat))\n",
    "print(\"Confidence Interval Estimates for the Variance of the active ingredient-concentration :\")\n",
    "ll = np.sqrt((n-1)*var_hat/chi2_upper)\n",
    "ul = np.sqrt((n-1)*var_hat/chi2_lower)\n",
    "#print(np.sqrt((n-1)*var_hat/chi2_upper))\n",
    "#print(np.sqrt((n-1)*var_hat/chi2_lower))\n",
    "print(round(ll,2)) \n",
    "print(round(ul,2))"
   ]
  }
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