Assignment-03-Q1 (Hypothesis Testing).ipynb

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 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Assignment-03-Q1 (Hypothesis Testing)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Q1. A F&B manager wants to determine whether there is any significant difference in the diameter of the cutlet between two units. A randomly selected sample of cutlets was collected from both units and measured? Analyze the data and draw inferences at 5% significance level. Please state the assumptions and tests that you carried out to check validity of the assumptions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   "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": 3,
   "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>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",
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      "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": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the dataset\n",
    "data=pd.read_csv('Database/Cutlets.csv')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Assume Null hyposthesis as Ho: μ1 = μ2 (There is no difference in diameters of cutlets between two units)\n",
    "Thus Alternate hypothesis as Ha: μ1 ≠ μ2 (There is significant difference in diameters of cutlets between two units)\n",
    "\n",
    "2 Sample 2 Tail test applicable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "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": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unitA=pd.Series(data.iloc[:,0])\n",
    "unitA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
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   "source": [
    "unitB=pd.Series(data.iloc[:,1])\n",
    "unitB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=0.7228688704678061, pvalue=0.47223947245995)"
      ]
     },
     "execution_count": 20,
     "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": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.47223947245995"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_value[1]     # 2-tail probability "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compare p_value with α = 0.05 (At 5% significance level)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Inference:\n",
    "As (p_value=0.4722) > (α = 0.05); Accept Null Hypothesis\n",
    "i.e. μ1 = μ2 (\n",
    "Thus, there is no difference in diameters of cutlets between two units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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