Assignment 3 - Hypothesis Testing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b7311afd",
   "metadata": {},
   "source": [
    "## HYPOTHESIS TESTING ASSIGNMENT"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57f3103d",
   "metadata": {},
   "source": [
    "### QUESTION 1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d94c7fd1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a36d9d98",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unit A</th>\n",
       "      <th>Unit B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.8090</td>\n",
       "      <td>6.7703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6.4376</td>\n",
       "      <td>7.5093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6.9157</td>\n",
       "      <td>6.7300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.3012</td>\n",
       "      <td>6.7878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7.4488</td>\n",
       "      <td>7.1522</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unit A  Unit B\n",
       "0  6.8090  6.7703\n",
       "1  6.4376  7.5093\n",
       "2  6.9157  6.7300\n",
       "3  7.3012  6.7878\n",
       "4  7.4488  7.1522"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the dataset\n",
    "data=pd.read_csv('dataset/Cutlets.csv')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8923125f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     6.8090\n",
       "1     6.4376\n",
       "2     6.9157\n",
       "3     7.3012\n",
       "4     7.4488\n",
       "5     7.3871\n",
       "6     6.8755\n",
       "7     7.0621\n",
       "8     6.6840\n",
       "9     6.8236\n",
       "10    7.3930\n",
       "11    7.5169\n",
       "12    6.9246\n",
       "13    6.9256\n",
       "14    6.5797\n",
       "15    6.8394\n",
       "16    6.5970\n",
       "17    7.2705\n",
       "18    7.2828\n",
       "19    7.3495\n",
       "20    6.9438\n",
       "21    7.1560\n",
       "22    6.5341\n",
       "23    7.2854\n",
       "24    6.9952\n",
       "25    6.8568\n",
       "26    7.2163\n",
       "27    6.6801\n",
       "28    6.9431\n",
       "29    7.0852\n",
       "30    6.7794\n",
       "31    7.2783\n",
       "32    7.1561\n",
       "33    7.3943\n",
       "34    6.9405\n",
       "Name: Unit A, dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unitA=pd.Series(data.iloc[:,0])\n",
    "unitA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "27b71e7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     6.7703\n",
       "1     7.5093\n",
       "2     6.7300\n",
       "3     6.7878\n",
       "4     7.1522\n",
       "5     6.8110\n",
       "6     7.2212\n",
       "7     6.6606\n",
       "8     7.2402\n",
       "9     7.0503\n",
       "10    6.8810\n",
       "11    7.4059\n",
       "12    6.7652\n",
       "13    6.0380\n",
       "14    7.1581\n",
       "15    7.0240\n",
       "16    6.6672\n",
       "17    7.4314\n",
       "18    7.3070\n",
       "19    6.7478\n",
       "20    6.8889\n",
       "21    7.4220\n",
       "22    6.5217\n",
       "23    7.1688\n",
       "24    6.7594\n",
       "25    6.9399\n",
       "26    7.0133\n",
       "27    6.9182\n",
       "28    6.3346\n",
       "29    7.5459\n",
       "30    7.0992\n",
       "31    7.1180\n",
       "32    6.6965\n",
       "33    6.5780\n",
       "34    7.3875\n",
       "Name: Unit B, dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unitB=pd.Series(data.iloc[:,1])\n",
    "unitB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "58cbc033",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=0.7228688704678063, pvalue=0.4722394724599501)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2-sample 2-tail ttest:   stats.ttest_ind(array1,array2)     # ind -> independent samples\n",
    "p_value=stats.ttest_ind(unitA,unitB)\n",
    "p_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ee49f8d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4722394724599501"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_value[1]     # 2-tail probability "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "252514a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# compare p_value with α = 0.05 (At 5% significance level)"
   ]
  },
   {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Accept Null Hypothesis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b544b0b8",
   "metadata": {},
   "source": [
    "### QUESTION 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0da3bcbb",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Laboratory 1</th>\n",
       "      <th>Laboratory 2</th>\n",
       "      <th>Laboratory 3</th>\n",
       "      <th>Laboratory 4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>185.35</td>\n",
       "      <td>165.53</td>\n",
       "      <td>176.70</td>\n",
       "      <td>166.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>170.49</td>\n",
       "      <td>185.91</td>\n",
       "      <td>198.45</td>\n",
       "      <td>160.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>192.77</td>\n",
       "      <td>194.92</td>\n",
       "      <td>201.23</td>\n",
       "      <td>185.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>177.33</td>\n",
       "      <td>183.00</td>\n",
       "      <td>199.61</td>\n",
       "      <td>176.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>193.41</td>\n",
       "      <td>169.57</td>\n",
       "      <td>204.63</td>\n",
       "      <td>152.60</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Laboratory 1  Laboratory 2  Laboratory 3  Laboratory 4\n",
       "0        185.35        165.53        176.70        166.13\n",
       "1        170.49        185.91        198.45        160.79\n",
       "2        192.77        194.92        201.23        185.18\n",
       "3        177.33        183.00        199.61        176.42\n",
       "4        193.41        169.57        204.63        152.60"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load the dataset\n",
    "data=pd.read_csv('dataset/LabTAT.csv')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0f623e0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "F_onewayResult(statistic=118.70421654401437, pvalue=2.1156708949992414e-57)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Anova ftest statistics: stats.f_oneway(column-1,column-2,column-3,column-4)\n",
    "p_value=stats.f_oneway(data.iloc[:,0],data.iloc[:,1],data.iloc[:,2],data.iloc[:,3])\n",
    "p_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "69da4a57",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.1156708949992414e-57"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_value[1]  # compare it with α = 0.05"
   ]
  },
   {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reject Null Hypothesis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "44de6a0f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "d6029fb1",
   "metadata": {},
   "source": [
    "### QUESTION 3 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b832b7bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "from scipy.stats import norm\n",
    "from scipy.stats import chi2_contingency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "776dc186",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Observed Values</th>\n",
       "      <th>East</th>\n",
       "      <th>West</th>\n",
       "      <th>North</th>\n",
       "      <th>South</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Males</td>\n",
       "      <td>50</td>\n",
       "      <td>142</td>\n",
       "      <td>131</td>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Females</td>\n",
       "      <td>435</td>\n",
       "      <td>1523</td>\n",
       "      <td>1356</td>\n",
       "      <td>750</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "  Observed Values  East  West  North  South\n",
       "0           Males    50   142    131     70\n",
       "1         Females   435  1523   1356    750"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load the dataset\n",
    "data= pd.read_csv('dataset/BuyerRatio.csv')\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "edf1b913",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  50,  142,  131,   70],\n",
       "       [ 435, 1523, 1356,  750]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make dimensional array\n",
    "obs=np.array([[50,142,131,70],[435,1523,1356,750]])\n",
    "obs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f183eb49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.595945538661058,\n",
       " 0.6603094907091882,\n",
       " 3,\n",
       " array([[  42.76531299,  146.81287862,  131.11756787,   72.30424052],\n",
       "        [ 442.23468701, 1518.18712138, 1355.88243213,  747.69575948]]))"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Chi2 contengency independence test\n",
    "chi2_contingency(obs) # o/p is (Chi2 stats value, p_value, df, expected obsvations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5997fb2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compare p_value with α = 0.05"
   ]
  },
   {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Accept Null Hypothesis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8e7d1cc0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "031ff7d6",
   "metadata": {},
   "source": [
    "### QUESTION 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "8baf34a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Phillippines</th>\n",
       "      <th>Indonesia</th>\n",
       "      <th>Malta</th>\n",
       "      <th>India</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Defective</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Defective</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Defective</td>\n",
       "      <td>Defective</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Defective</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>295</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>296</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>297</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Defective</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>298</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Defective</td>\n",
       "      <td>Defective</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>300 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Phillippines   Indonesia       Malta       India\n",
       "0     Error Free  Error Free   Defective  Error Free\n",
       "1     Error Free  Error Free  Error Free   Defective\n",
       "2     Error Free   Defective   Defective  Error Free\n",
       "3     Error Free  Error Free  Error Free  Error Free\n",
       "4     Error Free  Error Free   Defective  Error Free\n",
       "..           ...         ...         ...         ...\n",
       "295   Error Free  Error Free  Error Free  Error Free\n",
       "296   Error Free  Error Free  Error Free  Error Free\n",
       "297   Error Free  Error Free   Defective  Error Free\n",
       "298   Error Free  Error Free  Error Free  Error Free\n",
       "299   Error Free   Defective   Defective  Error Free\n",
       "\n",
       "[300 rows x 4 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load the dataset\n",
    "data=pd.read_csv('dataset/Costomer+OrderForm.csv')\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "71ac8ad7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Error Free    271\n",
       "Defective      29\n",
       "Name: Phillippines, dtype: int64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.Phillippines.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "00d188d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Error Free    267\n",
       "Defective      33\n",
       "Name: Indonesia, dtype: int64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.Indonesia.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "a03e56e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Error Free    269\n",
       "Defective      31\n",
       "Name: Malta, dtype: int64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.Malta.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "8525933a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Error Free    280\n",
       "Defective      20\n",
       "Name: India, dtype: int64"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.India.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "e0f7597c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[271, 267, 269, 280],\n",
       "       [ 29,  33,  31,  20]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make a contingency table\n",
    "obs=np.array([[271,267,269,280],[29,33,31,20]])\n",
    "obs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "d6ce3da2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.858960685820355,\n",
       " 0.2771020991233135,\n",
       " 3,\n",
       " array([[271.75, 271.75, 271.75, 271.75],\n",
       "        [ 28.25,  28.25,  28.25,  28.25]]))"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Chi2 contengency independence test\n",
    "chi2_contingency(obs) # o/p is (Chi2 stats value, p_value, df, expected obsvations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "44144dd7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compare p_value with α = 0.05"
   ]
  },
   {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Accept Null Hypothesis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7de97536",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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