Hypothesis_Testing.ipynb

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      "source": [
        "## Question 1"
      ],
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        "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"
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      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "from scipy import stats\n",
        "from scipy.stats import norm"
      ],
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      "source": [
        "df1 = pd.read_csv(\"/content/Cutlets.csv\")"
      ]
    },
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      "source": [
        "df1.head()"
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              "   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",
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        "da = df1[\"Unit A\"]\n",
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              "0.08317945374789916"
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          "execution_count": 182
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              "0.11792400440336127"
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        "t_stats , P_value = stats.ttest_ind(da, db, equal_var=False)"
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      "execution_count": 188,
      "outputs": []
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      "source": [
        "print(t_stats , P_value)"
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      "execution_count": 189,
      "outputs": [
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          "name": "stdout",
          "text": [
            "0.7228688704678063 0.47231324819145404\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "aplha = 0.05"
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      "execution_count": 190,
      "outputs": []
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      "cell_type": "code",
      "source": [
        "if P_value < aplha :\n",
        "  print(\"There is a significant difference between the two processes.\")\n",
        "else:\n",
        "  print(\"There is no significant difference between the two process.\")\n",
        ""
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          "text": [
            "There is no significant difference between the two process.\n"
          ]
        }
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      "source": [
        "## Question 2"
      ],
      "metadata": {
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        "A hospital wants to determine whether there is any difference in the average Turn Around Time (TAT) of reports of the laboratories on their preferred list. They collected a random sample and recorded TAT for reports of 4 laboratories. TAT is defined as sample collected to report dispatch.\n",
        "   \n",
        "  Analyze the data and determine whether there is any difference in average TAT among the different laboratories at 5% significance level."
      ],
      "metadata": {
        "id": "KwlLQ7oOrT4C"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df2 = pd.read_csv(\"/content/LabTAT.csv\")"
      ],
      "metadata": {
        "id": "moavly3Mrca5"
      },
      "execution_count": 150,
      "outputs": []
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        "df2"
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              "     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\n",
              "..            ...           ...           ...           ...\n",
              "115        178.49        170.66        193.80        172.68\n",
              "116        176.08        183.98        215.25        177.64\n",
              "117        202.48        174.54        203.99        170.27\n",
              "118        182.40        197.18        194.52        150.87\n",
              "119        182.09        215.17        221.49        162.21\n",
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              "    <tr>\n",
              "      <th>115</th>\n",
              "      <td>178.49</td>\n",
              "      <td>170.66</td>\n",
              "      <td>193.80</td>\n",
              "      <td>172.68</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>116</th>\n",
              "      <td>176.08</td>\n",
              "      <td>183.98</td>\n",
              "      <td>215.25</td>\n",
              "      <td>177.64</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>117</th>\n",
              "      <td>202.48</td>\n",
              "      <td>174.54</td>\n",
              "      <td>203.99</td>\n",
              "      <td>170.27</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>118</th>\n",
              "      <td>182.40</td>\n",
              "      <td>197.18</td>\n",
              "      <td>194.52</td>\n",
              "      <td>150.87</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>119</th>\n",
              "      <td>182.09</td>\n",
              "      <td>215.17</td>\n",
              "      <td>221.49</td>\n",
              "      <td>162.21</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>120 rows × 4 columns</p>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-e6d79c0c-6471-4422-b645-a8beeac3f57c')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-e6d79c0c-6471-4422-b645-a8beeac3f57c button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-e6d79c0c-6471-4422-b645-a8beeac3f57c');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-b31416d0-ae24-4e1b-9b33-909b06827561\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-b31416d0-ae24-4e1b-9b33-909b06827561')\"\n",
              "            title=\"Suggest charts.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-b31416d0-ae24-4e1b-9b33-909b06827561 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 151
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df2.describe()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "id": "PEfqzIFrr8dK",
        "outputId": "a201db4a-78a0-420e-f1d6-b530e067bc19"
      },
      "execution_count": 152,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       Laboratory 1  Laboratory 2  Laboratory 3  Laboratory 4\n",
              "count    120.000000    120.000000    120.000000     120.00000\n",
              "mean     178.361583    178.902917    199.913250     163.68275\n",
              "std       13.173594     14.957114     16.539033      15.08508\n",
              "min      138.300000    140.550000    159.690000     124.06000\n",
              "25%      170.335000    168.025000    188.232500     154.05000\n",
              "50%      178.530000    178.870000    199.805000     164.42500\n",
              "75%      186.535000    189.112500    211.332500     172.88250\n",
              "max      216.390000    217.860000    238.700000     205.18000"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-2654616a-2657-4efd-bc99-7121027c8d71\" class=\"colab-df-container\">\n",
              "    <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>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>count</th>\n",
              "      <td>120.000000</td>\n",
              "      <td>120.000000</td>\n",
              "      <td>120.000000</td>\n",
              "      <td>120.00000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>178.361583</td>\n",
              "      <td>178.902917</td>\n",
              "      <td>199.913250</td>\n",
              "      <td>163.68275</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>13.173594</td>\n",
              "      <td>14.957114</td>\n",
              "      <td>16.539033</td>\n",
              "      <td>15.08508</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>138.300000</td>\n",
              "      <td>140.550000</td>\n",
              "      <td>159.690000</td>\n",
              "      <td>124.06000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>170.335000</td>\n",
              "      <td>168.025000</td>\n",
              "      <td>188.232500</td>\n",
              "      <td>154.05000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>178.530000</td>\n",
              "      <td>178.870000</td>\n",
              "      <td>199.805000</td>\n",
              "      <td>164.42500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>186.535000</td>\n",
              "      <td>189.112500</td>\n",
              "      <td>211.332500</td>\n",
              "      <td>172.88250</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>216.390000</td>\n",
              "      <td>217.860000</td>\n",
              "      <td>238.700000</td>\n",
              "      <td>205.18000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-2654616a-2657-4efd-bc99-7121027c8d71')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-2654616a-2657-4efd-bc99-7121027c8d71 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-2654616a-2657-4efd-bc99-7121027c8d71');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-dd629a11-8797-44e2-bffb-8913d2cd69ef\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-dd629a11-8797-44e2-bffb-8913d2cd69ef')\"\n",
              "            title=\"Suggest charts.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
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              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-dd629a11-8797-44e2-bffb-8913d2cd69ef button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 152
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "lab1,lab2,lab3,lab4 = df2[\"Laboratory 1\"],df2[\"Laboratory 2\"],df2[\"Laboratory 3\"],df2[\"Laboratory 4\"]"
      ],
      "metadata": {
        "id": "qt5HIIxAsof7"
      },
      "execution_count": 153,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "aplha = 0.05"
      ],
      "metadata": {
        "id": "UZVdL0aTsGo4"
      },
      "execution_count": 154,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "F_sample , P_value1 = stats.f_oneway(lab1,lab2,lab3,lab4)\n",
        "print(F_sample , P_value1 )"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "t8GAL_1jsU6k",
        "outputId": "37d674c6-922a-4656-f963-8a54a90c3b5c"
      },
      "execution_count": 155,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "118.70421654401437 2.1156708949992414e-57\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "if P_value1 < aplha:\n",
        "  print(\"There is no difference in average TAT among the different laboratories\")\n",
        "else:\n",
        "  print(\"There is a difference in average TAT among the different laboratories\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2U4MjCzWtSci",
        "outputId": "2bd3e4b4-bbee-4893-8498-7c740bb938b2"
      },
      "execution_count": 156,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "There is no difference in average TAT among the different laboratories\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Question 3"
      ],
      "metadata": {
        "id": "Kic-qUUst7dl"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Sales of products in four different regions is tabulated for males and females. Find if male-female buyer rations are similar across regions."
      ],
      "metadata": {
        "id": "vsYbvjBlt7ZE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import statsmodels.api as sm\n",
        "import numpy as np\n",
        "import scipy.stats as stats"
      ],
      "metadata": {
        "id": "ac9iYbQfuKwh"
      },
      "execution_count": 157,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df03= pd.read_csv(\"/content/BuyerRatio.csv\")"
      ],
      "metadata": {
        "id": "TpRa01FAvI4T"
      },
      "execution_count": 158,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df03.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 112
        },
        "id": "B4vhBNVnyP-n",
        "outputId": "6ac89433-ce96-49ac-f95f-8f4a3636ba47"
      },
      "execution_count": 159,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "  Observed Values  East  West  North  South\n",
              "0           Males    50   142    131     70\n",
              "1         Females   435  1523   1356    750"
            ],
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              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
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              "  }\n",
              "\n",
              "  @keyframes spin {\n",
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              "      border-bottom-color: var(--fill-color);\n",
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              "\n",
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              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
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              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-b0552cd7-2347-43ff-8b25-b7afcf8d6add button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 159
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data = np.array([[50, 142, 131, 70], [435, 1523, 1356, 750]])"
      ],
      "metadata": {
        "id": "Sm6-o3Or03ID"
      },
      "execution_count": 160,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "chi2, p2, dof, expected = stats.chi2_contingency(data)"
      ],
      "metadata": {
        "id": "MVVVVOgazkYv"
      },
      "execution_count": 161,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "aplha = 0.05"
      ],
      "metadata": {
        "id": "GjqENoFw0NBr"
      },
      "execution_count": 162,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(f\"Chi-Square Statistic: {chi2}\")\n",
        "print(f\"P_value2: {p2}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UJojcocF0Bn8",
        "outputId": "4be12270-ebbf-48ea-a203-b395013cd74e"
      },
      "execution_count": 163,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Chi-Square Statistic: 1.595945538661058\n",
            "P_value2: 0.6603094907091882\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "if p2 < aplha:\n",
        "  print(\"male-female buyer rations are not similar across regions\")\n",
        "else:\n",
        "  print(\"male-female buyer rations are similar across regions\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "giDSJuiP6gwZ",
        "outputId": "9e382eba-ba24-4d1b-d913-800884b11922"
      },
      "execution_count": 178,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "male-female buyer rations are similar across regions\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Question 4"
      ],
      "metadata": {
        "id": "Ai64RK2h7nUj"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "TeleCall uses 4 centers around the globe to process customer order forms. They audit a certain %  of the customer order forms. Any error in order form renders it defective and has to be reworked before processing.  The manager wants to check whether the defective %  varies by centre. Please analyze the data at 5% significance level and help the manager draw appropriate inferences\n"
      ],
      "metadata": {
        "id": "kv-rM9ek7pyB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "from scipy.stats import chi2_contingency"
      ],
      "metadata": {
        "id": "-1i945i38_pJ"
      },
      "execution_count": 165,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df4 = pd.read_csv(\"/content/Costomer+OrderForm.csv\")"
      ],
      "metadata": {
        "id": "mEasusHo9DLr"
      },
      "execution_count": 166,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df4.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "Ko7uYCoX9KlC",
        "outputId": "49d902ee-d7d8-496c-94d8-466ec77ce5a5"
      },
      "execution_count": 173,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "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"
            ],
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              "      <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",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-dde284fc-b4a7-4080-9253-6a90e146909f')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
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              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-dde284fc-b4a7-4080-9253-6a90e146909f button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-dde284fc-b4a7-4080-9253-6a90e146909f');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-995efbc0-78b0-4e29-a96d-895795889132\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-995efbc0-78b0-4e29-a96d-895795889132')\"\n",
              "            title=\"Suggest charts.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
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              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
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              "    20% {\n",
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              "    }\n",
              "    30% {\n",
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              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-995efbc0-78b0-4e29-a96d-895795889132 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 173
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "contingency_table = pd.crosstab(df4['Phillippines'], [df4['Indonesia'], df4['Malta'], df4['India']])"
      ],
      "metadata": {
        "id": "5XpvVffl9MLA"
      },
      "execution_count": 168,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "chi2, p4, dof, expected = chi2_contingency(contingency_table)\n"
      ],
      "metadata": {
        "id": "arw1DXx49tzK"
      },
      "execution_count": 169,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Chi-Squared Statistic:\", chi2)\n",
        "print(\"P-value:\", p4)\n",
        "print(\"Degrees of Freedom:\", dof)\n",
        "print(\"Expected Frequencies Table:\")\n",
        "print(expected)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JoQ93aCZ9yZX",
        "outputId": "d9fe577c-e980-4ff6-ba9c-8338013ab5d0"
      },
      "execution_count": 170,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Chi-Squared Statistic: 3.1001395592512266\n",
            "P-value: 0.6845505149379718\n",
            "Degrees of Freedom: 5\n",
            "Expected Frequencies Table:\n",
            "[[8.70000000e-01 1.93333333e-01 2.12666667e+00 2.12666667e+00\n",
            "  1.74000000e+00 2.19433333e+01]\n",
            " [8.13000000e+00 1.80666667e+00 1.98733333e+01 1.98733333e+01\n",
            "  1.62600000e+01 2.05056667e+02]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "alpha = 0.05"
      ],
      "metadata": {
        "id": "wLfH1yYz953S"
      },
      "execution_count": 171,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "if p4 > alpha:\n",
        "    print(\"There is no significant association between call center and order form quality.\")\n",
        "else:\n",
        "    print(\"There is a significant association between call center and order form quality.\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IpLRI5eR98ez",
        "outputId": "91e9508e-8fa2-43c1-adb5-28ba70981ba3"
      },
      "execution_count": 176,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "There is no significant association between call center and order form quality.\n"
          ]
        }
      ]
    }
  ]
}