{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import scipy.stats\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Concepts of Hypothesis Testing </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You all heard of **null hypothesis** and **alternative hypothesis**, depends on the evidences that we decide to reject the null hypothesis or not. However if we do not have evidences to reject null hypothesis, we can't say that we accept null hypothesis, rather we say that _we can't reject null hypothesis based on current information_.\n",
    "\n",
    "Sometimes you might encounter the term of **type I error** and **type II error**, the former characterises the probability of rejecting a true null hypothesis, the latter characterises the probability of failing to reject a false null hypothesis. It might sounds counter-intuitive at first sight, but the plot below tells all story. \n",
    "\n",
    "The higher the significance level the lower probability of having type I error, but it increases the probability of having type II error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from plot_material import type12_error\n",
    "type12_error()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you are yet bewildered, here is the guideline, the blue shaded area are genuinely generated by null distribution, however they are too distant (i.e. $2\\sigma$ away) from the mean ($0$ in this example), so they are mistakenly rejected, this is what we call _Type I Error_. \n",
    "\n",
    "The orange shaded area are actually generated by alternative distribution, however they are in the adjacent area of mean of null hypothesis, so we failed to reject they, but wrongly. And this is called _Type II Error_.\n",
    "\n",
    "As you can see from the chart, if null distribution and alternative are far away from each other, the probability of both type of errors diminish to trivial. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Rejection Region and p-Value</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Rejection region** is a range of values such that if the test statistic falls into that range, we decide to reject the null hypothesis in favour of the alternative hypothesis.\n",
    "\n",
    "To put it another way, a value has to be far enough from the mean of null distribution to fall into rejection region, then the distance is the evidence that the value might not be produced by null distribution, therefore a rejection of null hypothesis.\n",
    "\n",
    "Let's use some real data for illustration. The data format is ```.csv```, best tool is ```pandas``` library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Gender</th>\n",
       "      <th>Height</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Index</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Male</td>\n",
       "      <td>174</td>\n",
       "      <td>96</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Male</td>\n",
       "      <td>189</td>\n",
       "      <td>87</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Female</td>\n",
       "      <td>185</td>\n",
       "      <td>110</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Female</td>\n",
       "      <td>195</td>\n",
       "      <td>104</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Male</td>\n",
       "      <td>149</td>\n",
       "      <td>61</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Gender  Height  Weight  Index\n",
       "0    Male     174      96      4\n",
       "1    Male     189      87      2\n",
       "2  Female     185     110      4\n",
       "3  Female     195     104      3\n",
       "4    Male     149      61      3"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('dataset/500_Person_Gender_Height_Weight_Index.csv')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Null and alternative hypothesis are\n",
    "$$\n",
    "H_0: \\text{Average male height is 172}\\newline\n",
    "H_1: \\text{Average male height isn't 172}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the sample mean and standard deviation of male height"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "male_mean = data[data['Gender']=='Male']['Height'].mean()\n",
    "male_std = data[data['Gender']=='Male']['Height'].std(ddof=1)\n",
    "male_std_error = male_std/np.sqrt(len(data[data['Gender']=='Male']))\n",
    "male_null = 172"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rejection region is simply an opposite view of expressing confidence interval\n",
    "$$\n",
    "\\bar{x}>\\mu + t_\\alpha\\frac{s}{\\sqrt{n}}\\\\\n",
    "\\bar{x}<\\mu - t_\\alpha\\frac{s}{\\sqrt{n}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assume significance level $5\\%$, then $+t_\\alpha = t_{.025}$ and $-t_{\\alpha} = t_{.975}$, where $t_{.025}$ and $t_{.975}$ can be calculated by ```.stat.t.ppf```."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9697339922715282"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = len(data[data['Gender']=='Male'])-1\n",
    "t_975 = sp.stats.t.ppf(.975, df=df); t_975"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.9697339922715287"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_025 = sp.stats.t.ppf(.025, df=df); t_025"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The rejection region of null hypothesis is <169.85242784779035 and >174.14757215220965\n"
     ]
    }
   ],
   "source": [
    "print('The rejection region of null hypothesis is <{} and >{}'.format(male_null - t_975*male_std_error, male_null + t_975*male_std_error))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "whereas the ```male_mean``` falls into\n",
    "the rejection region, we reject null hypothesis in favour of alternative hypothesis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "169.64897959183673"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "male_mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively we can construct $t$-statistic\n",
    "$$\n",
    "t=\\frac{\\bar{x}-\\mu}{s/\\sqrt{n}}\n",
    "$$\n",
    "Rejection region is where $t$-statistic larger or smaller than critical values\n",
    "$$\n",
    "t>t_{\\alpha} = t_{.025} \\text{   and   } t<t_{\\alpha} = t_{.975}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.1563349150893543"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = (male_mean - male_null)/(male_std_error); t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, the $t$ statistic falls short than critical value $t_{.025}$, which also tells that the sample mean deviates about $2.15$ standard errors away from the mean of null hypothesis, fairly significant evidence to reject null hypothesis. We also say the test is **statistically significant**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rejection region gives a yes or no answer, but **p-value** can give a probability how rare/extreme the test statistic is, given the null hypothesis is true. It can be easily retrieved by ```.stats.t.cdf``` function if the test statistic is negative as in our example, if positive then use ```1-.stats.t.cdf```. The p-value in our example is "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.016017555878266296"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.stats.t.cdf(t, df = df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It indicates that if $H_0 = 172$ is true, the probability of a sample mean of $169.64$ or smaller has around $1.6\\%$ probability. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> One- or Two-Tail Test</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The height example is a two-tail test, meaning constructing rejecting region on both sides, there are one-tail tests as well\n",
    "$$\n",
    "H_0: \\mu = \\mu_0\\\\\n",
    "H_1: \\mu > \\mu_0\n",
    "$$\n",
    "or \n",
    "$$\n",
    "H_0: \\mu = \\mu_0\\\\\n",
    "H_1: \\mu < \\mu_0\n",
    "$$\n",
    "Recall that in two-tail test, we divide the significance level by two, $2.5%$ on each side, but in one-tail test the significance level stays on either side as a whole.\n",
    "\n",
    "The figure below is the demonstration of one-tail test with $5\\%$ significance level on either side. The horizontal axis represents $t$-statistic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from plot_material import one_tail_rej_region_demo\n",
    "one_tail_rej_region_demo()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Inference About Difference Between Two Means</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the difference of means of two population is the primary concern, for instance we'd like to investigate whether man and women's starting salary level differs, we still can develop interval estimator and hypothesis test as in previous examples.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Two Population With Known $\\sigma_1$ and $\\sigma_2$</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The point estimator of the difference of two population means is\n",
    "$$\n",
    "\\bar{x}_1-\\bar{x}_2\n",
    "$$\n",
    "and its standard error is \n",
    "$$\n",
    "\\sigma_{\\bar{x}_{1}-\\bar{x}_{2}}=\\sqrt{\\frac{\\sigma_{1}^{2}}{n_{1}}+\\frac{\\sigma_{2}^{2}}{n_{2}}}\n",
    "$$\n",
    "if both populations have a normal distribution, then sampling distribution of $\\bar{x}_1-\\bar{x}_2$ also have a normal distribution. Then the $z$ statistic has a normal distribution\n",
    "$$\n",
    "z=\\frac{\\left(\\bar{x}_{1}-\\bar{x}_{2}\\right)-(\\mu_1-\\mu_2)}{\\sqrt{\\frac{\\sigma_{1}^{2}}{n_{1}}+\\frac{\\sigma_{2}^{2}}{n_{2}}}}\n",
    "$$\n",
    "\n",
    "The interval estimator with known $\\sigma_1$ and $\\sigma_2$ is constructed by rearranging $z$-statistic\n",
    "$$\n",
    "\\bar{x}_{1}-\\bar{x}_{2} \\pm z_{\\alpha / 2} \\sqrt{\\frac{\\sigma_{1}^{2}}{n_{1}}+\\frac{\\sigma_{2}^{2}}{n_{2}}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can simulate a case of population height, first create two populations of male and female with $\\mu_1 = 175$ and $\\mu_2 = 170$, also $\\sigma_1=10$ and $\\sigma_2=8$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Point estimate of the difference of the population means is 7.37.\n",
      "Confidence interval of the difference of the population means is (4.86, 9.88).\n"
     ]
    }
   ],
   "source": [
    "male_population = sp.stats.norm.rvs(loc=175,scale=10,size=10000) # generate male population of 10000\n",
    "female_population = sp.stats.norm.rvs(loc=170,scale=8,size=10000) # generate famale population of 10000\n",
    "\n",
    "male_sample = np.random.choice(male_population, 100) # take sample\n",
    "female_sample = np.random.choice(female_population, 100)\n",
    "\n",
    "male_sample_mean = np.mean(male_sample) \n",
    "female_sample_mean = np.mean(female_sample)\n",
    "\n",
    "standard_error = np.sqrt(10**2/100+8**2/100) \n",
    "\n",
    "LCL = male_sample_mean-female_sample_mean - sp.stats.norm.ppf(.975)*standard_error # lower confidence level\n",
    "UCL = male_sample_mean-female_sample_mean + sp.stats.norm.ppf(.975)*standard_error\n",
    "\n",
    "print('Point estimate of the difference of the population means is {:.2f}.'.format(male_sample_mean-female_sample_mean))\n",
    "print('Confidence interval of the difference of the population means is ({:.2f}, {:.2f}).'.format(LCL, UCL))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are three forms of hypothesis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{array}{lll}\n",
    "H_{0}: \\mu_{1}-\\mu_{2} \\geq D_{0} & H_{0}: \\mu_{1}-\\mu_{2} \\leq D_{0} & H_{0}: \\mu_{1}-\\mu_{2}=D_{0} \\\\\n",
    "H_{\\mathrm{1}}: \\mu_{1}-\\mu_{2} < D_{0} & H_{\\mathrm{1}}: \\mu_{1}-\\mu_{2}>D_{0} & H_{\\mathrm{1}}: \\mu_{1}-\\mu_{2} \\neq D_{0}\n",
    "\\end{array}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $z$ statistic test has the same mechanism as in one population inference, we would like to know how many standard deviation away from the null hypothesis of difference of population mean.\n",
    "$$\n",
    "z=\\frac{\\left(\\bar{x}_{1}-\\bar{x}_{2}\\right)-D_{0}}{\\sqrt{\\frac{\\sigma_{1}^{2}}{n_{1}}+\\frac{\\sigma_{2}^{2}}{n_{2}}}}=\\frac{\\left(\\bar{x}_{1}-\\bar{x}_{2}\\right)-(\\mu_1-\\mu_2)}{\\sqrt{\\frac{\\sigma_{1}^{2}}{n_{1}}+\\frac{\\sigma_{2}^{2}}{n_{2}}}}\n",
    "$$\n",
    "Back to our example, suppose our hypothesis is the men and women has the same average height\n",
    "$$\n",
    "H_0:\\mu_1-\\mu_2 = 0\\\\\n",
    "H_1:\\mu_1-\\mu_2 \\neq 0\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We actually know that we will reject null hypothesis, because data generation parameter is $\\mu_1=175$ and $\\mu_2=170$, here is the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "z statistic: 5.76\n",
      "p-Value: 4.299676725771917e-09\n"
     ]
    }
   ],
   "source": [
    "z = ((male_sample_mean - female_sample_mean) - 0)/standard_error\n",
    "p_value = 1 - sp.stats.norm.cdf(z)\n",
    "print('z statistic: {:.2f}'.format(z))\n",
    "print('p-Value: {}'.format(p_value))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We reject the null hypothesis $\\mu_1=\\mu_2$ in favour of alternative hypothesis $\\mu_1\\neq\\mu_2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Two Population With Unknown $\\sigma_1$ and $\\sigma_2$</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you have guess, interval estimator with two population with unknown $\\sigma_1$ and $\\sigma_2$ is \n",
    "$$\n",
    "\\bar{x}_{1}-\\bar{x}_{2} \\pm t_{\\alpha / 2} \\sqrt{\\frac{s_{1}^{2}}{n_{1}}+\\frac{s_{2}^{2}}{n_{2}}}\n",
    "$$\n",
    "And $t$-statistic\n",
    "$$\n",
    "t=\\frac{\\left(\\bar{x}_{1}-\\bar{x}_{2}\\right)-D_{0}}{\\sqrt{\\frac{s_{1}^{2}}{n_{1}}+\\frac{s_{2}^{2}}{n_{2}}}}\n",
    "$$\n",
    "However the degree of freedom has a nastier form\n",
    "$$\n",
    "d f=\\frac{\\left(\\frac{s_{1}^{2}}{n_{1}}+\\frac{s_{2}^{2}}{n_{2}}\\right)^{2}}{\\frac{1}{n_{1}-1}\\left(\\frac{s_{1}^{2}}{n_{1}}\\right)^{2}+\\frac{1}{n_{2}-1}\\left(\\frac{s_{2}^{2}}{n_{2}}\\right)^{2}}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Besides that, rest of procedures are the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degree of freedom: 194\n",
      "t-statistic: 5.7895\n",
      "Confidence interval of the difference of the population means is (4.86, 9.88).\n"
     ]
    }
   ],
   "source": [
    "male_sample_variance = np.var(male_sample, ddof=1)\n",
    "female_sample_variance = np.var(female_sample, ddof=1)\n",
    "\n",
    "standard_error_unknown = np.sqrt(male_sample_variance/100+female_sample_variance/100)\n",
    "df = standard_error_unknown**4/(1/99*(male_sample_variance/100)**2 + 1/99*(female_sample_variance/100)**2)\n",
    "\n",
    "LCL = male_sample_mean-female_sample_mean - sp.stats.t.ppf(.975, df=df)*standard_error_unknown\n",
    "UCL = male_sample_mean-female_sample_mean + sp.stats.t.ppf(.975, df=df)*standard_error_unknown\n",
    "\n",
    "print('Degree of freedom: {:.0f}'.format(df))\n",
    "print('t-statistic: {:.4f}'.format(((male_sample_mean - female_sample_mean) - 0)/standard_error_unknown))\n",
    "print('Confidence interval of the difference of the population means is ({:.2f}, {:.2f}).'.format(LCL, UCL))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Inference About Difference Between Two Population Proportions</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is one of most widely used inference technique in business field. We will introduce it by walking through an example. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Do Banks Discriminate Against Women Clients?</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A market research company just surveyed $3139$ business owners, of whom $649$ are female. $59$ women were turned down when applying for a business loan, in contrast $128$ men were turned down.\n",
    "\n",
    "What we would like to know is if banks have possible gender bias?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The sample proportions of loan rejections are\n",
    "$$\n",
    "\\hat{p}_1=\\frac{59}{649}=9.0\\%\\\\\n",
    "\\hat{p}_2=\\frac{128}{2490}=5.1\\%\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where $\\hat{p}_1$ and $\\hat{p}_2$ are rejection proportion of women and men respectively.\n",
    "\n",
    "You certainly can stop here and report these numbers with a conclusion that women clients are indeed discriminated. But we can also take a more scientific attitude, to minimise the possibility of a fluke. Therefore we continue the hypothesis testing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hypotheses specified as\n",
    "$$\n",
    "H_0: p_1 - p_2=0\\\\\n",
    "H_1:  p_1 - p_2>0\n",
    "$$\n",
    "If we know $p_1$ and $p_2$, the standard error of sample distribution of $\\hat{p}_1-\\hat{p}_2$ is \n",
    "$$\n",
    "\\sigma_{\\hat{p}_1-\\hat{p}_2}=\\sqrt{\\frac{p_1(1-p_1)}{n_1}+\\frac{p_2(1-p_2)}{n_2}}\n",
    "$$\n",
    "Unfortunately, we know nothing about them. However null hypothesis $p_1=p_2$ allows us to formulate a **pooled proportion estimate**,\n",
    "$$\n",
    "\\hat{p}=\\frac{x_1+x_2}{n_1+n_1}\n",
    "$$\n",
    "The standard error becomes\n",
    "$$\n",
    "\\sigma_{\\hat{p}_1-\\hat{p}_2}=\\sqrt{\\hat{p}(1-\\hat{p})\\bigg(\\frac{1}{n_1}+\\frac{1}{n_2}\\bigg)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pooled proportion estimates is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_hat = (59 + 128)/(649 + 2490)\n",
    "sigma = np.sqrt(p_hat*(1-p_hat)*(1/649+1/2490))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Value of test statistic is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "z=\\frac{\\hat{p}_1-\\hat{p}_2}{\\sqrt{\\hat{p}(1-\\hat{p})\\bigg(\\frac{1}{n_1}+\\frac{1}{n_2}\\bigg)}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test statistic of z is 3.7386.\n"
     ]
    }
   ],
   "source": [
    "z = (.09-0.051)/sigma\n",
    "print('Test statistic of z is {:.4f}.'.format(z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Without checking the critical value, we could safely conclude a fail to null hypothesis after seeing a test statistic great than $3$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Inference About A Population Variance</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Previously we have seen the pointer estimator of $\\sigma^2$ is \n",
    "$$\n",
    "s^2=\\frac{\\Sigma\\left(x_{i}-\\bar{x}\\right)^{2}}{n-1}\n",
    "$$\n",
    "However because of a square, it doesn't have the familiar normal or $t$-statistic. The test statistic of $\\sigma^2$ has a $\\chi^2$ distribution\n",
    "$$\n",
    "\\chi^2=\\frac{(n-1) s^{2}}{\\sigma^{2}_0}\n",
    "$$\n",
    "with $\\nu =n-1$ degree of freedom. With some algebraic manipulation, the confidence interval estimator of $95\\%$ confidence level is\n",
    "$$\n",
    "\\frac{(n-1) s^{2}}{\\chi_{.025}^{2}} \\leq \\sigma^{2} \\leq \\frac{(n-1) s^{2}}{\\chi_{.975}^{2}}\n",
    "$$\n",
    "where $\\chi^2_{0.025}$\n",
    "To use our generated population height data, let's assume we want to know if variance of female height is less than $50$, hypotheses are\n",
    "$$\n",
    "H_0: \\sigma^2 \\geq 50\\\\\n",
    "H_1: \\sigma^2 <50\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Female sample variance: 69.42919661941376\n",
      "Chi-square statistic: 138.85839323882752.\n",
      "p-value: 0.9948934676592497.\n",
      "Confidence interval: (53.52, 93.69)\n"
     ]
    }
   ],
   "source": [
    "chi_square_statistic = len(female_sample)*female_sample_variance/50\n",
    "df = len(female_sample)-1\n",
    "LCL = df*female_sample_variance/sp.stats.chi2.ppf(.975, df=df)\n",
    "UCL = df*female_sample_variance/sp.stats.chi2.ppf(.025, df=df)\n",
    "print('Female sample variance: {}'.format(female_sample_variance))\n",
    "print('Chi-square statistic: {}.'.format(chi_square_statistic))\n",
    "print('p-value: {}.'.format(sp.stats.chi2.cdf(chi_square_statistic, df=df)))\n",
    "print('Confidence interval: ({:.2f}, {:.2f})'.format(LCL, UCL))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hypothesis test states that we don't have evidence to reject null hypothesis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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