E-News Project.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Context:\n",
    "An online news portal aims to expand its business by acquiring new subscribers. Every visitor to the website takes certain actions based on their interest. The company plans to analyze these interests and wants to determine whether a new feature will be effective or not. Companies often analyze users' responses to two variants of a product to decide which of the two variants is more effective. This experimental technique is known as a/b testing that is used to determine whether a new feature attracts users based on a chosen metric.\n",
    "\n",
    "# Objective:     \n",
    "Perform statistical analysis to answer the following questions:\n",
    "\n",
    "1. Explore the dataset and extract insights using Exploratory Data Analysis.\n",
    "2. Do the users spend more time on the new landing page than the old landing page?\n",
    "3. Is the conversion rate for the new page greater than the conversion rate for the old page?\n",
    "4. Does the converted status depend on the preferred language?\n",
    "5. Is the mean time spent on the new page same for the different language users?\n",
    "\n",
    "Note: significance level of 0.05 is considered for all tests\n",
    "\n",
    "# Data Dictionary:\n",
    "1. user_id - This represents the user ID of the person visiting the website.\n",
    "2. group - This represents whether the user belongs to the first group (control) or the second group (treatment).\n",
    "3. landing_page - This represents whether the landing page is new or old.\n",
    "4. time_spent_on_the_page - This represents the time (in minutes) spent by the user on the landing page.\n",
    "5. converted - This represents whether the user gets converted or not.\n",
    "6. language_preferred - This represents the language chosen by the user to view the landing page."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import the necessary packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore') \n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import scipy.stats as stats\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Read the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"abtest.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### View the first and last 5 rows of the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
       "      <th>group</th>\n",
       "      <th>landing_page</th>\n",
       "      <th>time_spent_on_the_page</th>\n",
       "      <th>converted</th>\n",
       "      <th>language_preferred</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>546592</td>\n",
       "      <td>control</td>\n",
       "      <td>old</td>\n",
       "      <td>3.48</td>\n",
       "      <td>yes</td>\n",
       "      <td>Spanish</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>546468</td>\n",
       "      <td>treatment</td>\n",
       "      <td>new</td>\n",
       "      <td>7.13</td>\n",
       "      <td>yes</td>\n",
       "      <td>English</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>546462</td>\n",
       "      <td>treatment</td>\n",
       "      <td>new</td>\n",
       "      <td>4.40</td>\n",
       "      <td>no</td>\n",
       "      <td>Spanish</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>546567</td>\n",
       "      <td>control</td>\n",
       "      <td>old</td>\n",
       "      <td>3.02</td>\n",
       "      <td>no</td>\n",
       "      <td>French</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>546459</td>\n",
       "      <td>treatment</td>\n",
       "      <td>new</td>\n",
       "      <td>4.75</td>\n",
       "      <td>yes</td>\n",
       "      <td>Spanish</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   user_id      group landing_page  time_spent_on_the_page converted  \\\n",
       "0   546592    control          old                    3.48       yes   \n",
       "1   546468  treatment          new                    7.13       yes   \n",
       "2   546462  treatment          new                    4.40        no   \n",
       "3   546567    control          old                    3.02        no   \n",
       "4   546459  treatment          new                    4.75       yes   \n",
       "\n",
       "  language_preferred  \n",
       "0            Spanish  \n",
       "1            English  \n",
       "2            Spanish  \n",
       "3             French  \n",
       "4            Spanish  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head() # displays the first five rows of the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\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>user_id</th>\n",
       "      <th>group</th>\n",
       "      <th>landing_page</th>\n",
       "      <th>time_spent_on_the_page</th>\n",
       "      <th>converted</th>\n",
       "      <th>language_preferred</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>546446</td>\n",
       "      <td>treatment</td>\n",
       "      <td>new</td>\n",
       "      <td>5.15</td>\n",
       "      <td>no</td>\n",
       "      <td>Spanish</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>546544</td>\n",
       "      <td>control</td>\n",
       "      <td>old</td>\n",
       "      <td>6.52</td>\n",
       "      <td>yes</td>\n",
       "      <td>English</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>546472</td>\n",
       "      <td>treatment</td>\n",
       "      <td>new</td>\n",
       "      <td>7.07</td>\n",
       "      <td>yes</td>\n",
       "      <td>Spanish</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>546481</td>\n",
       "      <td>treatment</td>\n",
       "      <td>new</td>\n",
       "      <td>6.20</td>\n",
       "      <td>yes</td>\n",
       "      <td>Spanish</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>546483</td>\n",
       "      <td>treatment</td>\n",
       "      <td>new</td>\n",
       "      <td>5.86</td>\n",
       "      <td>yes</td>\n",
       "      <td>English</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    user_id      group landing_page  time_spent_on_the_page converted  \\\n",
       "95   546446  treatment          new                    5.15        no   \n",
       "96   546544    control          old                    6.52       yes   \n",
       "97   546472  treatment          new                    7.07       yes   \n",
       "98   546481  treatment          new                    6.20       yes   \n",
       "99   546483  treatment          new                    5.86       yes   \n",
       "\n",
       "   language_preferred  \n",
       "95            Spanish  \n",
       "96            English  \n",
       "97            Spanish  \n",
       "98            Spanish  \n",
       "99            English  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.tail() # displays the last five rows of the dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Checking the shape and data types of the columns for the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 6)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The dataset has 180 rows and 9 columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 100 entries, 0 to 99\n",
      "Data columns (total 6 columns):\n",
      " #   Column                  Non-Null Count  Dtype  \n",
      "---  ------                  --------------  -----  \n",
      " 0   user_id                 100 non-null    int64  \n",
      " 1   group                   100 non-null    object \n",
      " 2   landing_page            100 non-null    object \n",
      " 3   time_spent_on_the_page  100 non-null    float64\n",
      " 4   converted               100 non-null    object \n",
      " 5   language_preferred      100 non-null    object \n",
      "dtypes: float64(1), int64(1), object(4)\n",
      "memory usage: 4.8+ KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fixing the data types\n",
    "* group, landing_page, converted and language_preferred are of object type, we can change them to category.\n",
    "\n",
    "`coverting \"objects\" to \"category\" reduces the data space required to store the dataframe`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"group\"]=df[\"group\"].astype(\"category\")\n",
    "df[\"landing_page\"]=df[\"landing_page\"].astype(\"category\")\n",
    "df[\"converted\"]=df[\"converted\"].astype(\"category\")\n",
    "df[\"language_preferred\"]=df[\"language_preferred\"].astype(\"category\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 100 entries, 0 to 99\n",
      "Data columns (total 6 columns):\n",
      " #   Column                  Non-Null Count  Dtype   \n",
      "---  ------                  --------------  -----   \n",
      " 0   user_id                 100 non-null    int64   \n",
      " 1   group                   100 non-null    category\n",
      " 2   landing_page            100 non-null    category\n",
      " 3   time_spent_on_the_page  100 non-null    float64 \n",
      " 4   converted               100 non-null    category\n",
      " 5   language_preferred      100 non-null    category\n",
      "dtypes: category(4), float64(1), int64(1)\n",
      "memory usage: 2.5 KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* group, landing_page, converted and language_preferred have been converted to categories\n",
    "\n",
    "`we can see that the memory usage has decreased from 4.8+ KB to 2.5 KB`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Statistical summary for the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "\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>user_id</th>\n",
       "      <th>time_spent_on_the_page</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>546517.000000</td>\n",
       "      <td>5.377800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>52.295779</td>\n",
       "      <td>2.378166</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>546443.000000</td>\n",
       "      <td>0.190000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>546467.750000</td>\n",
       "      <td>3.880000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>546492.500000</td>\n",
       "      <td>5.415000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>546567.250000</td>\n",
       "      <td>7.022500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>546592.000000</td>\n",
       "      <td>10.710000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             user_id  time_spent_on_the_page\n",
       "count     100.000000              100.000000\n",
       "mean   546517.000000                5.377800\n",
       "std        52.295779                2.378166\n",
       "min    546443.000000                0.190000\n",
       "25%    546467.750000                3.880000\n",
       "50%    546492.500000                5.415000\n",
       "75%    546567.250000                7.022500\n",
       "max    546592.000000               10.710000"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* time_spent_on_the_page has approximately same mean and median."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\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>group</th>\n",
       "      <th>landing_page</th>\n",
       "      <th>converted</th>\n",
       "      <th>language_preferred</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>treatment</td>\n",
       "      <td>old</td>\n",
       "      <td>yes</td>\n",
       "      <td>Spanish</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>50</td>\n",
       "      <td>50</td>\n",
       "      <td>55</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            group landing_page converted language_preferred\n",
       "count         100          100       100                100\n",
       "unique          2            2         2                  3\n",
       "top     treatment          old       yes            Spanish\n",
       "freq           50           50        55                 34"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe(include=[\"category\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* group and landing_page categories are equally divided.\n",
    "* converted (55) represent more users got converted to the enews.\n",
    "* language_preferred has 3 unique categories which indicates there are 3 languages."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Checking for Missing Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "user_id                   0\n",
       "group                     0\n",
       "landing_page              0\n",
       "time_spent_on_the_page    0\n",
       "converted                 0\n",
       "language_preferred        0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* There are no missing values in the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Exploratory Data Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Writing a function to help create boxplot and histogram for any input numerical variable.\n",
    "# This function takes the numerical column as the input and returns the boxplots and histograms for the variable.\n",
    "\n",
    "def histogram_boxplot(feature, figsize=(12,7), bins = None):\n",
    "    f2, (ax_box2, ax_hist2) = plt.subplots(nrows = 2, sharex = True, figsize = figsize, \n",
    "                                           gridspec_kw = {\"height_ratios\": (.25, .75)})\n",
    "    sns.boxplot(feature, ax=ax_box2, showmeans=True, color='violet')\n",
    "    sns.distplot(feature, kde=False, ax=ax_hist2, bins=bins)\n",
    "    ax_hist2.axvline(np.mean(feature), color='green', linestyle='--')\n",
    "    ax_hist2.axvline(np.median(feature), color='black', linestyle='-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Observations on time spent on the page"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5BZggH7n6xL4jAAyaC94AABgN5RcAgNFQfgEAGA3lFwCA0XDBG8AEefnD/ypJ8t68ueckAMOk/AJMkD133KfvCACDpvwCTJALV3227wgAg6b8AkyQT17z7r4jAAyaC94AABgN5RcAgNFQfgEAGA3lFwCA0XDBG8AEedV+f58kOSmv6zkJwDApvwAT5De237PvCACDpvwCTJCv3vDxviMADJryCzBBzr32tL4jAAyaC94AABgN5RcAgNFQfgEAGA3lFwCA0VB+ASbI0QeclKMPOKnvGACD5W4PABPkvtvs0ncEgEFTfgEmyBdWntl3BIBBU34BJsgXrzur7wgAg2bOLwAAo6H8AgAwGsovAACjofwCADAayi/ABDlm6Sk5ZukpfccAGCx3ewCYINtutX3fEQAGTfkFmCDnXPu+viMADNpGpz1U1XuralVVXT5t7C+q6rqqurj784z5jQkwDstvODvLbzi77xgAg7Upc35PSfL0dYz/fWtt/+7PJ+c2FgAAzL2Nlt/W2nlJbtoCWQAAYF7N5m4Pr6mqS7tpETuvb6GqOrKqVlTVitWrV89icwAAMDszLb8nJdknyf5Jbkjyt+tbsLV2cmttaWtt6aJFi2a4OQAAmL0Zld/W2o9aa3e11u5O8u4kB81tLIBxesvBp+ctB5/edwyAwZpR+a2qPaY9fU6Sy9e3LAAATIqN3ue3qj6Q5AlJdq2qlUmOTfKEqto/SUvyvSR/MH8RAcbj7Gve1XcEgEHbaPltrT1/HcPvmYcsAKN30ar/6DsCwKDN5m4PAACwoCi/AACMhvILAMBobHTOLwBbzr232jZJ8svc3nMSgGFSfmEOvH/5tX1HYCDeuPR9SZK3veeInpMADJNpDwAAjIYzvwAT5MNXndB3BIBBU34BJsgVP/5K3xEABs20BwAARkP5BQBgNJRfAABGw5xfgAmy4zY7JUluzc295gAYKuUXYIK89oB3JUneFvf5BZgPpj0AADAazvwCTJAPfuudfUcAGDTlF2CCXHXzhX1HWPB83PjmecHBe/cdAbYo0x4AABgN5RcAgNFQfgEAGA1zfgEmyC7b/WaS5Kb8sOckAMOk/AJMkFc/4oQk7vMLMF9MewAAYDSc+QWYIP925V/2HQFg0JRfgAny/Z99o+8IAINm2gMAAKOh/AIAMBrKLwAAo2HOL8AE+c0dHpAk+WGu6TkJwDApvwAT5P/u+44k7vMLMF9MewAAYDSc+QWYIP9y+Zv6jgAwaMovwAT54c/N9QWYT6Y9AAAwGsovAACjofwCADAa5vwCTJD7/9rDkiTfzzd6TgIwTMovwAR58UOPTeI+vwDzxbQHAABGw5lfgAnyz5cc3XcEgEFTfgEmyE2/+GHfEQAGzbQHAABGQ/kFAGA0lF8AAEbDnF+ACfJbOz0ySXJVLuw5CcAwbfTMb1W9t6pWVdXl08Z2qapzquo73ded5zcmwDg878FvzPMe/Ma+YwAM1qZMezglydPXGntTknNbaw9Mcm73HAAAJtpGpz201s6rqiVrDT87yRO6x6cm+XwSpyoAZukfLvqDviMADNpM5/zu3lq7IUlaazdU1W7rW7CqjkxyZJLsvffeM9wcwDjcesfNfUdgZN6//Nq+IywoLzhYl1no5v1uD621k1trS1trSxctWjTfmwMAgPWaafn9UVXtkSTd11VzFwkAAObHTMvvx5K8tHv80iQfnZs4AAAwfzY657eqPpCpi9t2raqVSY5N8o4kZ1TVK5Jcm+Tw+QwJMBYP/43HJkmuyFd6TgIwTJtyt4fnr+elJ81xFoDRe85vHZ1E+QWYLz7eGACA0fDxxgAT5J0rXtJ3BIBBU34BJsgv77q97wgAg2baAwAAo6H8AgAwGsovAACjYc4vwAQ5YLcnJkkuyn/0nARgmJRfgAnyzAf8QRLlF2C+mPYAAMBoOPMLMEHetvyIviMADJozvwAAjIbyCwDAaCi/AACMhvILAMBouOANYIIcvMczkyTLc3bPSQCGSfkFmCBP2fslSZRfgPmi/AJMkNvvuq3vCACDpvwCTJDjV7ys7wgAg+aCNwAARkP5BQBgNJRfAABGQ/kFAGA0XPAGMEEev/i5SZIv5qyekwAMk/ILMEH+5/0OT6L8AswX5Rdggtxyx019RwAYNOUXYIKccNGr+o4AMGgueAMAYDRGceb3/cuv7TsCAAATwJlfAABGQ/kFAGA0RjHtAWCheNLeL0qSnJvTek4CMEzO/AJMkMfs8aw8Zo9n9R0DYLCc+QWYID++7fq+IwAMmvILMEFOuvR1fUcAGDTTHgAAGA3lFwCA0VB+AQAYDeUXAIDRcMEbwAR5xgNemST5ZN7dcxKAYXLmF2CCPHK3J+eRuz257xgAg+XML8AEuf7Wq/uOADBoyi/ABHnvFW/uOwLAoJn2AADAaCi/AACMhvILAMBozGrOb1V9L8ktSe5KcmdrbelchAIAgPkwFxe8/a/W2o1zsB6A0Tt0n6OSJB/JiT0nARgm0x4AJsi+uz4u++76uL5jAAzWbM/8tiSfqaqW5F2ttZPXXqCqjkxyZJLsvffes9wcwLB972dX9B0BYNBmW34Paa1dX1W7JTmnqr7ZWjtv+gJdIT45SZYuXdpmuT2AQTvtyuP6jgAwaLOa9tBau777uirJh5McNBehAABgPsy4/FbVDlV13zWPkzw1yeVzFQwAAObabKY97J7kw1W1Zj3vb619ak5SAQDAPJhx+W2tfTfJI+YwCwAAzKu5uM8vAHPk9x90TJLkjBzfcxKAYVJ+ASbIg3b2QZkA80n5BZgg3/7Jir4jAAya8gswQc74tukOAPPJxxsDADAazvwCAGyi9y+/tu8IC8oLDt677wj34MwvAACjofwCADAapj0ATJAXPfStSZLTclzPSQCGSfkFmCBLfu3hfUcAGDTlF2CCXH7jl/qOADBoyi/ABPnI1Sf2HQFg0FzwBgDAaCi/AACMhvILAMBoKL8AAIyGC94AJsjLH/5XSZL35s09JwEYJuUXYILsueM+fUcAGDTlF2CCXLjqs31HABg05Rdggnzymnf3HQFg0FzwBgDAaCi/AACMhvILAMBoKL8AAIyGC94AJsir9vv7JMlJeV3PSQCGSfkFmCC/sf2efUcAGDTlF2CCfPWGj/cdAWDQlF+ACXLutaf1HQFg0FzwBgDAaCi/AACMhvILAMBoKL8AAIyG8gswQY4+4KQcfcBJfccAGCx3ewCYIPfdZpe+IwAMmvILMEG+sPLMviMADJryCzBBvnjdWX1HABg0c34BABgN5RcAgNFQfgEAGA3lFwCA0VB+ASbIMUtPyTFLT+k7BsBgudsDwATZdqvt+44AMGjKL8AEOefa9/UdAWDQlF+ACbL8hrP7jgAwaOb8AgAwGrMqv1X19Kr6VlVdVVVvmqtQAAAwH2ZcfqtqqyT/lOR/J3lYkudX1cPmKhgAAMy12Zz5PSjJVa2177bW7kjywSTPnptYAAAw92ZzwdviJD+Y9nxlkoPXXqiqjkxyZPf01qr61iy2Od2uSW6co3XRP8dzWBzPOfLCR9+/7wiJ4zkkjuWwTPzxfGG/m1/nD9DZlN9ax1i7x0BrJyc5eRbbWffGq1a01pbO9Xrph+M5LI7nsDiew+FYDovjOTOzmfawMsle057fL8n1s4sDAADzZzbl9+tJHlhVD6iqbZI8L8nH5iYWAADMvRlPe2it3VlVr0ny6SRbJXlva+2KOUu2cXM+lYJeOZ7D4ngOi+M5HI7lsDieM1Ct3WOaLgAADJJPeAMAYDSUXwAARmNBll8fqzwcVbVXVX2uqq6sqiuq6ui+MzE7VbVVVV1UVZ/oOwuzU1U7VdVZVfXN7v/Rx/SdiZmrqtd1P2cvr6oPVNV2fWdi01XVe6tqVVVdPm1sl6o6p6q+033duc+MC8WCK78+Vnlw7kzyJ621hyZ5dJI/cjwXvKOTXNl3CObECUk+1Vp7SJJHxHFdsKpqcZI/TrK0tbZvpi5Uf16/qdhMpyR5+lpjb0pybmvtgUnO7Z6zEQuu/MbHKg9Ka+2G1tqF3eNbMvWX6+J+UzFTVXW/JM9M8i99Z2F2qurXkvx2kvckSWvtjtbazb2GYra2TrJ9VW2d5D5xb/4FpbV2XpKb1hp+dpJTu8enJjl0S2ZaqBZi+V3XxyorSwNQVUuSHJBkec9RmLl/SPL/ktzdcw5m738kWZ3kX7tpLP9SVTv0HYqZaa1dl+Rvklyb5IYkP22tfabfVMyB3VtrNyRTJ5OS7NZzngVhIZbfTfpYZRaWqtoxyYeSvLa19rO+87D5qup3kqxqrV3QdxbmxNZJHpnkpNbaAUl+Hr9SXbC6uaDPTvKAJHsm2aGqXtRvKujHQiy/PlZ5YKrq3pkqvv/eWlvWdx5m7JAkv1tV38vUdKQnVtVp/UZiFlYmWdlaW/ObmLMyVYZZmJ6c5JrW2urW2i+TLEvy2J4zMXs/qqo9kqT7uqrnPAvCQiy/PlZ5QKqqMjWn8MrW2t/1nYeZa639aWvtfq21JZn6//I/WmvOLC1QrbUfJvlBVT24G3pSkm/0GInZuTbJo6vqPt3P3SfFBYxD8LEkL+0evzTJR3vMsmDM+OON+zIBH6vM3DokyYuTXFZVF3djb26tfbK/SEDnqCT/3p1o+G6S/9NzHmaotba8qs5KcmGm7rJzUXw07oJSVR9I8oQku1bVyiTHJnlHkjOq6hWZ+gfO4f0lXDh8vDEAAKOxEKc9AADAjCi/AACMhvILAMBoKL8AAIyG8gsAwGgovwAAjIbyCywYVbVTVb26e7xnd9/SBamqDq2qh22B7exfVc+Y9vwvquoN871dgEml/AILyU5JXp0krbXrW2vP7TfOrByaZN7Lb5L9kzxjYwsBjIXyCywk70iyT1VdXFVnVtXlSVJVL6uqj1TVx6vqmqp6TVW9vqouqqrzq2qXbrl9qupTVXVBVX2xqh6yvg1V1eFVdXlVXVJV503bzke7dXyrqo6dtvyLquprXbZ3VdVW3fitVfX2bj3nV9XuVfXYJL+b5Phu+X3Wk2H/7j2XVtWHq2rnbvzzVfXObnvfrqrHr+f92yQ5LskR3XaO6F56WLeO71bVH29sH9az7lur6m+r6sKqOreqFnXjr6yqr3f7+6Gqus+07/353WvHVdWt09Z1TDd+aVX95fq2CTAXlF9gIXlTkqtba/snOWat1/ZN8oIkByV5e5L/bK0dkOSrSV7SLXNykqNaawcmeUOSf97Att6a5GmttUdkqqiucVCSF2bqjOrhVbW0qh6a5Igkh3TZ7uqWSZIdkpzfree8JK9srX0lyceSHNNa27+1dvV6MrwvyRtba/sluSxTH2e6xtattYOSvHat8V9prd3R7cfp3XZO7156SJKndftybFXdeyP7sC47JLmwtfbIJF+YlmFZa+1R3f5emeQV3fgJSU5orT0qyfVrVlJVT03ywC7L/kkOrKrf3sB2AWZl674DAMyRz7XWbklyS1X9NMnHu/HLkuxXVTsmeWySM6tqzXu23cD6vpzklKo6I8myaePntNZ+nCRVtSzJ45LcmeTAJF/v1r19klXd8nck+UT3+IIkT9mUnamqX0+yU2vtC93QqUnOnLbImkwXJFmyKeuc5uzW2u1Jbq+qVUl2T/KkDezDutydZE2ZPm1ann2r6m2ZmqKyY5JPd+OPydRUjyR5f5K/6R4/tftzUfd8x0yV4fM2c58ANonyCwzF7dMe3z3t+d2Z+ll3ryQ3d2c1N6q19odVdXCSZya5uKrWvK+tvWiSSnJqa+1P17GqX7bW1rznrszdz901+zeTdU7/Xq15/4b2YVOs2cdTkhzaWrukql6W5AkbeV8l+evW2rtmuF2AzWLaA7CQ3JLkvjN5Y2vtZ0muqarDk6SmPGJ9y1fVPq215a21tya5Mcle3UtPqapdqmr7TJ3J/HKSc5M8t6p26967S1Xdfzb70lr7aZKfTJvP++JMTS/YXJv6PdvcfbhXkjUXHL4gyZe6x/dNckNV3Tv/fdrE+Ul+r3v8vGnjn07y8u7MfKpq8ZoMAPNB+QUWjG66wZe7C92On8EqXpjkFVV1SZIrkjx7A8seX1WXdds6L8kl3fiXkvxbkouTfKi1tqK19o0kb0nymaq6NMk5SfbYSJYPJjmmuyhvnRe8JXlpl+PSTM2HPW5jO7gOn8vUBW7TL3i7hxnsw8+TPLyqLkjyxGnZ/jzJ8u7935y2/GuTvL6qvtat96fddj+TqWkQX62qy5KclRn+AwdgU9R//TYOgA3pfo2/tLX2mr6z9K2qbm2t7bgZy98nyW2ttVZVz0vy/Nbahv7xATAvzPkFYEs4MMk/1tTVdDcneXm/cYCxcuYXGLWq+rMkh681fGZr7e1bMMM/JTlkreETWmv/uhnreFqSd641fE1r7TmzzLY897wrxotba5fNZr0AfVF+AQAYDRe8AQAwGsovAACjofwCADAayi8AAKPx/wFjdCkZxvq0SAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "histogram_boxplot(df[\"time_spent_on_the_page\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Mean time spent on the page by users is 5.37\n",
    "* There are no outliers present in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAE9CAYAAADXtxyoAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAeh0lEQVR4nO3dfbRWdZ338fdXBMknTDjjNGMEOo2liaCMZfgYDWjjMDI+Nz5lhTU2ONOtFeNt6szYXaN3y7FR75gJIh9GRdNyMqWxCG1yBBQRI0ONCi1FFAVTVPjef5wNnU7I2Rz2PtfZh/drrb3Ofvzt73XW4uJzfnvv347MRJIkSdXZptUFSJIk9TUGLEmSpIoZsCRJkipmwJIkSaqYAUuSJKliBixJkqSKbdvqAjoaMmRIDhs2rNVlSJIkdWn+/PnPZmbbxrb1qoA1bNgw5s2b1+oyJEmSuhQRP3ujbV4ilCRJqlitASsi9oqIBR2mFyPib+s8pyRJUqvVeokwMx8FRgJERD/gSeDWOs8pSZLUaj15D9ZY4PHMfMPrlRvz2muvsWzZMl555ZWayuodBg4cyO67707//v1bXYokSdpCPRmwTgL+o/PKiJgETAIYOnTo7xy0bNkydtppJ4YNG0ZE1F5kK2QmK1asYNmyZQwfPrzV5UiSpC3UIze5R8QAYAIws/O2zJyamaMzc3Rb2+8+6fjKK68wePDgPhuuACKCwYMH9/leOkmSthY99RThUcADmfl0dw7uy+Fqva3hM0qStLXoqYB1Mhu5PNhkK1eu5Kqrrtrs4y666CIuu+yyGiqSJEm9Re0BKyK2B/4U+Hrd5+opa9eu7XbAkiRJfV/tASszf52ZgzPzhSrb/drXvsaIESPYb7/9OPXUU/nZz37G2LFjGTFiBGPHjuXnP/85AGeccQaTJ0/mve99L3vssQc333wzACeeeCJ33HHHhvbOOOMMbrnlFtauXct5553Hn/zJnzBixAi+/OUvAzB79myOOOIIPvjBD7Lvvvvymc98hscff5yRI0dy3nnnAXDppZduOO7CCy/c0PYll1zCXnvtxfvf/34effTRKn8NkiSpF+pVr8op65FHHuGSSy7hBz/4AUOGDOG5557j9NNP57TTTuP0009n2rRpTJ48mdtuuw2AX/7yl9x77738+Mc/ZsKECRx33HGcdNJJ3HjjjXzgAx/g1Vdf5e677+bqq6/mK1/5CoMGDWLu3LmsWbOGMWPGMG7cOADuv/9+Fi1axPDhw1m6dCmLFi1iwYIFAMyaNYslS5Zw//33k5lMmDCBOXPmsMMOO3DDDTfw4IMP8vrrr7P//vtzwAEHtOg3J0mSekIjA9Z3v/tdjjvuOIYMGQLArrvuyg9/+EO+/vX2q5Cnnnoqn/rUpzbsf8wxx7DNNtuw99578/TT7ffZH3XUUUyePJk1a9Zw5513cuihh/KmN72JWbNmsXDhwg09XS+88AJLlixhwIABHHjggW84jMKsWbOYNWsWo0aNAmD16tUsWbKEVatWMXHiRLbffnsAJkyYUM8vRZJUieUzz251CdoCbcdf2eoSgIYGrMzs8qm7jtu322673zoW2gf2PPzww7nrrru48cYbOfnkkzds/9KXvsT48eN/q73Zs2ezww47bLKmKVOmcNZZZ/3W+ssvv9wnBCVJ2so08mXPY8eO5aabbmLFihUAPPfcc7z3ve/lhhtuAOC6667j4IMP7rKdk046ienTp3PPPfdsCFTjx4/n6quv5rXXXgPgJz/5CS+99NLvHLvTTjuxatWqDcvjx49n2rRprF69GoAnn3ySZ555hkMPPZRbb72Vl19+mVWrVnH77bdv2YeXJEm9XiN7sPbZZx/OP/98DjvsMPr168eoUaO44oorOPPMM7n00ktpa2tj+vTpXbYzbtw4TjvtNCZMmMCAAQMA+MhHPsLSpUvZf//9yUza2to23MvV0eDBgxkzZgzvete7OOqoo7j00ktZvHgxBx10EAA77rgj1157Lfvvvz8nnngiI0eO5G1vexuHHHJIpb8LSZLU+8T6S2a9wejRo3PevHm/tW7x4sW8853vbFFFPWtr+qyS1Ft5D1az9eQ9WBExPzNHb2xbIy8RSpIk9WYGLEmSpIoZsCRJkipmwJIkSaqYAUuSJKliBixJkqSKGbAkSZIq1siBRtdbfvbMSttru/L4StuTJElbJ3uwNtPSpUt55zvfyUc/+lH22Wcfxo0bx8svv8yCBQt4z3vew4gRI5g4cSLPP/98q0uVJEktYsDqhiVLlnD22WfzyCOPsMsuu3DLLbdw2mmn8YUvfIGFCxey7777cvHFF7e6TEmS1CIGrG4YPnw4I0eOBOCAAw7g8ccfZ+XKlRx22GEAnH766cyZM6eFFUqSpFYyYHXDdtttt2G+X79+rFy5snXFSJKkXseAVYFBgwbx5je/mXvuuQeAa665ZkNvliRJ2vo0+inC3mTGjBl87GMf49e//jV77LEH06dPb3VJkiSpRRodsFoxrMKwYcNYtGjRhuVzzz13w/x9993X4/VIkqTex0uEkiRJFTNgSZIkVcyAJUmSVDEDliRJUsUMWJIkSRUzYEmSJFXMgCVJklSxRo+DtXzm2ZW213b8lZW2J0mStk61B6yI2AX4d+BdQAJnZuYP6z5vHS644AKGDBnCOeecA8D555/Pbrvtxpo1a7jppptYs2YNEydO5OKLL+all17ihBNOYNmyZaxdu5YLLriAE088scWfQJIk9YSeuET4L8CdmfkOYD9gcQ+csxYf/vCHmTFjBgDr1q3jhhtuYLfddmPJkiXcf//9LFiwgPnz5zNnzhzuvPNO/uAP/oCHHnqIRYsWceSRR7a4ekmS1FNq7cGKiJ2BQ4EzADLzVeDVOs9Zp2HDhjF48GAefPBBnn76aUaNGsXcuXOZNWsWo0aNAmD16tUsWbKEQw45hHPPPZdPf/rTHH300RxyyCEtrl6SJPWUui8R7gEsB6ZHxH7AfOCczHxp/Q4RMQmYBDB06NCay9lyH/nIR/jqV7/Kr371K84880zuvvtupkyZwllnnfU7+86fP5877riDKVOmMG7cOD772c+2oGJJktTT6r5EuC2wP3B1Zo4CXgI+03GHzJyamaMzc3RbW1vN5Wy5iRMncueddzJ37lzGjx/P+PHjmTZtGqtXrwbgySef5JlnnuGpp55i++2355RTTuHcc8/lgQceaHHlkiSpp9Tdg7UMWJaZ/1Ms30yngNU0AwYM4IgjjmCXXXahX79+jBs3jsWLF3PQQQcBsOOOO3Lttdfy2GOPcd5557HNNtvQv39/rr766hZXLkmSekqtASszfxURv4iIvTLzUWAs8KOq2m/FsArr1q3jvvvuY+bMmRvWnXPOORueLFxvzz33ZPz48T1dniRJ6gV6YhysvwGui4gBwBPAh3rgnLX40Y9+xNFHH83EiRN5+9vf3upytnpVj4OmnuW4c5L6stoDVmYuAEbXfZ6esPfee/PEE0+0ugxJktTL+aocSZKkijUiYGVmq0uo3dbwGSVJ2lr0+oA1cOBAVqxY0acDSGayYsUKBg4c2OpSJElSBXr9y5533313li1bxvLly1tdSq0GDhzI7rvv3uoyJElSBXp9wOrfvz/Dhw9vdRmSJEml9fpLhJIkSU1jwJIkSaqYAUuSJKliBixJkqSKGbAkSZIqZsCSJEmqmAFLkiSpYgYsSZKkihmwJEmSKmbAkiRJqpgBS5IkqWIGLEmSpIoZsCRJkipmwJIkSaqYAUuSJKliBixJkqSKGbAkSZIqZsCSJEmqmAFLkiSpYgYsSZKkihmwJEmSKlY6YEXEwRHxoWK+LSKG11eWJElSc21bZqeIuBAYDewFTAf6A9cCY+orTZKaafnZM1tdgrbE4a0uQH1BqYAFTARGAQ8AZOZTEbFTmQMjYimwClgLvJ6Zo7tRpyRJUmOUDVivZmZGRAJExA6beZ4jMvPZzTxGkiSpkcreg3VTRHwZ2CUiPgr8F/Bv9ZUlSZLUXKV6sDLzsoj4U+BF2u/D+mxmfqfkORKYVfR+fTkzp3avVEmSpGYoe4mQIlCVDVUdjSnu2fo94DsR8ePMnLN+Y0RMAiYBDB06tBvNS5Ik9S6lLhFGxKqIeLHT9IuIuDUi9tjUsZn5VPHzGeBW4MBO26dm5ujMHN3W1tbdzyFJktRrlO3B+iLwFHA9EMBJwO8DjwLTeIOHWoub4bfJzFXF/DjgH7awZkmSpF6tbMA6MjPf3WF5akTcl5n/EBF/v4njdgNujYj157o+M+/sZq2SJEmNUDZgrYuIE4Cbi+XjOmzLNzooM58A9utmbZIkSY1UdpiGvwJOBZ4Bni7mT4mINwGfqKk2SZKkRio7TMMTwJ+/weZ7qytHkiSp+cq+i3Ag8GFgH2Dg+vWZeWZNdUmSJDVW2UuE19D+1OB44PvA7rS/X1CSJEmdlA1Yf5SZFwAvZeYM4M+AfesrS5IkqbnKBqzXip8rI+JdwCBgWC0VSZIkNVzZYRqmRsSbgQuAbwI7FvOSJEnqpOxThP9ezH4f2OSrcSRJkrZ2Zd9FODgivhQRD0TE/Ii4PCIG112cJElSE5W9B+sG2gcZPZb2UdyfBW6sqyhJkqQmK3sP1q6Z+Y8dlv8pIo6poR5JkqTGK9uD9b2IOCkitimmE4Bv1VmYJElSU5UNWGcB1wNriukG4JMRsSoiXqyrOEmSpCYq+xThTpvaHhH7ZOYj1ZQkSZLUbGV7sLpyTUXtSJIkNV5VASsqakeSJKnxqgpYWVE7kiRJjVdVwJIkSVKhqoD1akXtSJIkNV7ZV+VERJwSEZ8tlodGxIHrt2fme+oqUJIkqWnK9mBdBRwEnFwsrwKurKUiSZKkhiv7qpx3Z+b+EfEgQGY+HxEDaqxLkiSpscr2YL0WEf0onhaMiDZgXW1VSZIkNVjZgHUFcCvwexFxCXAv8LnaqpIkSWqwsq/KuS4i5gNjaR9U9JjMXFxrZZIkSQ1V9h4sgCXAi+uPiYihmfnzWqqSJElqsFIBKyL+BrgQeBpYS3svVgIj6itNkiSpmcr2YJ0D7JWZK+osRpIkqS8oe5P7L4AX6ixEkiSpr9hkD1ZEfLKYfQKYHRHfAtas356ZXyxzkmKIh3nAk5l5dDdrlSRJaoSuLhHuVPz8eTENKCYoxsQq6RxgMbDzZlUnSZLUQJsMWJl5MUBEHJ+ZMztui4jjy5wgInYH/gy4BPhkF7tLkiQ1Xtl7sKaUXLcxlwOfwpHfJUnSVqKre7COAj4A/GFEXNFh087A6101HhFHA89k5vyIOPwN9pkETAIYOnRouaolSZJ6sa56sJ6i/eb0V4D5HaZvAuNLtD8GmBARS4EbgPdFxLUdd8jMqZk5OjNHt7W1bWb5kiRJvU9X92A9BDwUEddn5mtvtF9E3JKZx27k+CkUlxKLHqxzM/OULapYkiSplyt1D9amwlVhjwpqkSRJ6hM2512Em9LlkA2ZORuYXdH5JEmSeq2yTxFKkiSppKoCVlTUjiRJUuNVFbA+XVE7kiRJjVfqHqyIGANcBLytOCaAzMw9aJ+ZVVeBkiRJTVP2JvevAH9H+xhYa+srR5IkqfnKBqwXMvPbtVYiSZLUR5QNWN+LiEuBrwNr1q/MzAdqqUqSJKnBygasdxc/R3dYl8D7qi1HkiSp+UoFrMw8ou5CJEmS+opSwzRExKCI+GJEzCum/xsRg+ouTpIkqYnKjoM1DVgFnFBMLwLT6ypKkiSpycreg7VnZh7bYfniiFhQQz2SJEmNV7YH6+WIOHj9QjHw6Mv1lCRJktRsZXuwPgZ8rcN9V88Dp9dTkiRJUrOVfYrwIWC/iNi5WH6x4/aIOD0zZ9RQnyRJUuNs1sueM/PFzuGqcE5F9UiSJDXeZgWsTYiK2pEkSWq8qgJWVtSOJElS49mDJUmSVLFSN7lHxPDM/Okm1v2g8sp6wPKzZ7a6BG2Jw1tdgCRJG1e2B+uWjay7ef1MZn6imnIkSZKab5M9WBHxDmAfYFBE/GWHTTsDA+ssTJIkqam6ukS4F3A0sAvw5x3WrwI+WlNNkiRJjbbJgJWZ3wC+EREHZeYPe6gmSZKkRiv7qpzHIuLvgWEdj8nMM+soSpIkqcnKBqxvAPcA/wWsra8cSZKk5isbsLbPzE/XWokkSVIfUXaYhv+MiA/UWokkSVIfUTZgnUN7yHolIl6MiFURsbGXPkuSJG31Sl0izMydutN4RAwE5gDbFee6OTMv7E5bkiRJTVGqByvanRIRFxTLb42IA0scugZ4X2buB4wEjoyI93S7WkmSpAYoe4nwKuAg4IPF8mrgyq4Oynari8X+xZSbW6QkSVKTlA1Y787Ms4FXADLzeWBAmQMjol9ELACeAb6Tmf/TnUIlSZKaomzAei0i+lH0PkVEG7CuzIGZuTYzRwK7AwdGxLs6bo+ISRExLyLmLV++vHzlkiRJvVTZgHUFcCuwW0RcAtwLfG5zTpSZK4HZwJGd1k/NzNGZObqtrW1zmpQkSeqVyj5FeF1EzAfGFquOyczFXR1X9HS9lpkrI+JNwPuBL3S7WkmSpAYoO5I7wPbA+suEbyp5zFuAGcXlxW2AmzLzPzevREmSpGYpFbAi4rPA8cAtQADTI2JmZv7Tpo7LzIXAqC2uUpIkqUHK9mCdDIzKzFcAIuLzwAPAJgOWJEnS1qjsTe5LgYEdlrcDHq+8GkmSpD6gbA/WGuCRiPgO7fdg/Slwb0RcAZCZk2uqT5IkqXHKBqxbi2m92dWXIkmS1DeUHaZhxvr5iHgz8NbiBnZJkiR1UvZlz7MjYueI2BV4iPanCL9Yb2mSJEnNVPYm90GZ+SLwl8D0zDyA9kFDJUmS1EnZgLVtRLwFOAFwoFBJkqRNKBuw/gG4C3gsM+dGxB7AkvrKkiRJaq5SASszZ2bmiMz862L5icw8dv32iJhSV4GSJElNU7YHqyvHV9SOJElS41UVsKKidiRJkhqvqoCVFbUjSZLUePZgSZIkVayqgDWzonYkSZIar+xI7n8cEXdHxKJieURE/O/12zPzc3UVKEmS1DRle7D+DZgCvAZQvIfwpLqKkiRJarKyAWv7zLy/07rXqy5GkiSpLygbsJ6NiD0pnhaMiOOAX9ZWlSRJUoNtW3K/s4GpwDsi4kngp8AptVUlSZLUYKUCVmY+Abw/InYAtsnMVfWWJUmS1FylAlZE7AKcBgwDto1oH/YqMyfXVZgkSVJTlb1EeAdwH/AwsK6+ciRJkpqvbMAamJmfrLUSSZKkPqLsU4TXRMRHI+ItEbHr+qnWyiRJkhqqbA/Wq8ClwPn85sXOCexRR1GSJElNVjZgfRL4o8x8ts5iJEmS+oKylwgfAX5dZyGSJEl9RdkerLXAgoj4HrBm/UqHaZAkSfpdZQPWbcW0WSLircDXgN+nfXiHqZn5L5vbjiRJUpOUHcl9Rjfbfx34X5n5QETsBMyPiO9k5o+62Z4kSVKvt8mAFRE3ZeYJEfEwv3l6cL3MzP02dXxm/pLipdCZuSoiFgN/CBiwJElSn9VVD9Y5xc/FwHkd1gfwz5tzoogYBowC/mdzjpMkSWqaTQasogcK2odo+FnHbRHxjrIniYgdgVuAv83MFzttmwRMAhg6dGjZJiVJknqtTQ7TEBEfLy4P7hURCztMPwUWljlBRPSnPVxdl5lf77w9M6dm5ujMHN3W1tadzyBJktSrdHWJ8Hrg28D/AT7TYf2qzHyuq8YjIoCvAIsz84vdrlKSJKlBurpE+ALwAnByN9sfA5wKPBwRC4p1f5+Zd3SzPUmSpF6v7DhY3ZKZ99J+Q7wkSdJWo+yrciRJklSSAUuSJKliBixJkqSKGbAkSZIqZsCSJEmqmAFLkiSpYgYsSZKkihmwJEmSKmbAkiRJqpgBS5IkqWIGLEmSpIoZsCRJkipmwJIkSaqYAUuSJKliBixJkqSKGbAkSZIqZsCSJEmqmAFLkiSpYgYsSZKkihmwJEmSKmbAkiRJqpgBS5IkqWIGLEmSpIoZsCRJkipmwJIkSaqYAUuSJKliBixJkqSKGbAkSZIqZsCSJEmqWK0BKyKmRcQzEbGozvNIkiT1JnX3YH0VOLLmc0iSJPUqtQaszJwDPFfnOSRJknob78GSJEmqWMsDVkRMioh5ETFv+fLlrS5HkiRpi7U8YGXm1MwcnZmj29raWl2OJEnSFmt5wJIkSepr6h6m4T+AHwJ7RcSyiPhwneeTJEnqDbats/HMPLnO9iVJknojLxFKkiRVzIAlSZJUMQOWJElSxQxYkiRJFTNgSZIkVcyAJUmSVDEDliRJUsUMWJIkSRUzYEmSJFXMgCVJklQxA5YkSVLFDFiSJEkVM2BJkiRVzIAlSZJUMQOWJElSxQxYkiRJFTNgSZIkVcyAJUmSVDEDliRJUsUMWJIkSRUzYEmSJFXMgCVJklQxA5YkSVLFDFiSJEkVM2BJkiRVzIAlSZJUMQOWJElSxQxYkiRJFTNgSZIkVaz2gBURR0bEoxHxWER8pu7zSZIktVqtASsi+gFXAkcBewMnR8TedZ5TkiSp1eruwToQeCwzn8jMV4EbgL+o+ZySJEktVXfA+kPgFx2WlxXrJEmS+qxta24/NrIuf2uHiEnApGJxdUQ8WnNN6iuuYgjwbKvLUHdd1eoCpI3zu6XhevS75W1vtKHugLUMeGuH5d2BpzrukJlTgak116E+KCLmZeboVtchqW/xu0VVqPsS4Vzg7RExPCIGACcB36z5nJIkSS1Vaw9WZr4eEZ8A7gL6AdMy85E6zylJktRqdV8iJDPvAO6o+zzaKnlpWVId/G7RFovM7HovSZIklearciRJkipmwFJjRcSwiPhgN447IyL+tY6aJNUrInaJiL/ubW31hvOodzFgqcmGARsNWBFR+/2FklpiF+B3wkrxarZK2qpBT51HvYgBSy0TEadFxMKIeCgiromIt0XE3cW6uyNiaLHfVyPiioj474h4IiKOK5r4PHBIRCyIiL8reqZmRsTtwKyI2DUibivauy8iRrTsw0qqyueBPYt/93Mj4nsRcT3wcET0i4hLi/ULI+IsgIjYsfhOeSAiHo6Iv9hIW5dGxOER8f2IuCkifhIRn4+Iv4qI+4vj9izaa4uIW4rzzI2IMcX6iyJiWkTMLr6rJm/sPD3761LLZKaTU49PwD7Ao8CQYnlX4Hbg9GL5TOC2Yv6rwEza/yDYm/b3WwIcDvxnhzbPoH1w212L5S8BFxbz7wMWdNjvX1v9O3Byctr8ifae60XF/OHAS8DwYnkS8L+L+e2AecBw2p+Y37lYPwR4jPY3jWxoq0N7K4G3FMc/CVxcbDsHuLyYvx44uJgfCiwu5i8C/rs4dgiwAujf+TxOW8fkZRS1yvuAmzPzWYDMfC4iDgL+sth+DfDPHfa/LTPXAT+KiN020e53MvO5Yv5g4Nii/e9GxOCIGFTpp5DUavdn5k+L+XHAiA693IOAt9P+h9fnIuJQYB3t78R9o++RuZn5S4CIeByYVax/GDiimH8/sHfEhrfB7RwROxXz38rMNcCaiHhmE+dRH2fAUqsEnd5LuREdt6/pdOwbeamL/RyXROpbOv+b/5vMvKvjDhFxBtAGHJCZr0XEUmDgG7TX8btmXYfldfzm/8xtgIMy8+VO5+l8/Fr8f3ar5T1YapW7gRMiYjBAROxKe9f6ScX2vwLu7aKNVcBOm9g+p2iHiDgceDYzX+x+yZJ6gU39u78L+HhE9AeIiD+OiB1o78l6pghXR/CbF/R29R3yRmYBn1i/EBEjt6Bm9VEma7VEZj4SEZcA34+ItcCDwGRgWkScBywHPtRFMwuB1yPiIdrv03q+0/aLgOkRsRD4NXB6dZ9AUitk5oqI+EFELAJeBp7usPnfab/f6YFo705aDhwDXAfcHhHzgAXAjzfS1reBb5UsYzJwZfHdsi3tf8x9rGTN387M88p+XjWXI7lLkiRVzEuEkiRJFTNgSZIkVcyAJUmSVDEDliRJUsUMWJIkSRUzYEmSJFXMgCWpz4kIx/iT1FKOgyWpcSLiAtpH6f8F8CwwHzia9rcBjAG+SfuAkpfRPhDkXODjmbmmeE3K6Mx8NiJGA5dl5uERcRGwJ+3vqXsr8M+Z+W89+bkk9R3+lSepUYpQdCwwivbvsAdoD1gAu2TmYRExEFgCjM3Mn0TE14CPA5d30fwI4D3ADsCDEfGtzHyqho8hqY/zEqGkpjkY+EZmvpyZq4DbO2y7sfi5F/DTzPxJsTwDOLRE2+vbfRb4HnBgVUVL2roYsCQ1TWxi20sl9nmd33z3Dey0rfM9E95DIalbDFiSmuZe4M8jYmBE7Aj82Ub2+TEwLCL+qFg+Ffh+Mb8UOKCYP7bTcX9RtDsYOJz2e7ckabMZsCQ1SmbOpf0m9oeArwPzgBc67fMK8CFgZkQ8DKwD/l+x+WLgXyLiHmBtp+bvB74F3Af8o/dfSeounyKU1DgRsWNmro6I7YE5wKTMfGAL27wIWJ2Zl1VRo6Stm08RSmqiqRGxN+33UM3Y0nAlSVWzB0uSJKli3oMlSZJUMQOWJElSxQxYkiRJFTNgSZIkVcyAJUmSVDEDliRJUsX+P8p48XKlSJy3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "sns.barplot(data=df, x='group', y='time_spent_on_the_page', hue='converted', palette='spring', ci=None)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Converted users in both groups spend more time on the landing page."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "sns.barplot(data=df, x='landing_page', y='time_spent_on_the_page', palette='spring', ci=None)\n",
    "plt.show()\n",
    "plt.figure(figsize=(10,5))\n",
    "sns.barplot(data=df, x='landing_page', y='time_spent_on_the_page', palette='spring', \n",
    "            hue=df[\"language_preferred\"],  ci=None)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Users who land on the new page spends more time on the page than users who land on the old page.\n",
    "* Users with English as preferred language spend the most time on the new page and users with Spanish as preferred language spend the most time on the old page."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Observations on converted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "sns.countplot(df[\"converted\"], palette='gnuplot2_r');\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(10,5))\n",
    "sns.countplot(df[\"converted\"], hue=df[\"language_preferred\"], palette='gnuplot2_r');\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(10,5))\n",
    "sns.countplot(df[\"landing_page\"], hue=df['converted'], palette='gnuplot2_r');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* In general, there are more converted users.\n",
    "* Users who prefer to view in English have the highest rate of converted users.\n",
    "* Users who prefer to view in French have the highest rate of non-converted users.\n",
    "* Conversion rate for the new page is greater than the conversion rate for the old page"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Observations on language preferred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "sns.countplot(df[\"language_preferred\"], palette='winter');\n",
    "plt.show()\n",
    "plt.figure(figsize=(10,5))\n",
    "sns.stripplot(data=df, x='language_preferred', y='time_spent_on_the_page')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Lesser users prefer to view the landing page in English compared to users that prefer viewing in French and Spanish.\n",
    "* Users who prefer to view in Spanish spend lesser time on the landing page compared to the other preferred languages."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Do the users spend more time on the new landing page than the old landing page?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hypothesis Formulation;\n",
    "\n",
    "Using the two independent sample t-test\n",
    "\n",
    "* $H_0: \\mu_{new} = \\mu_{old}$ (Users don't spend more time on the new landing page)\n",
    "\n",
    "* $H_a: \\mu_{new} > \\mu_{old}$ (Users spend more time on the new landing page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "sns.boxplot(x=\"landing_page\", y=\"time_spent_on_the_page\", data=df, palette='vlag')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The p-value is  0.0001316123528095005\n"
     ]
    }
   ],
   "source": [
    "# Perform two independent sample t-test\n",
    "\n",
    "from scipy.stats import ttest_ind\n",
    "\n",
    "test_stat, p_value = ttest_ind(df.loc[df['landing_page'] == 'new', 'time_spent_on_the_page'],\n",
    "                              df.loc[df['landing_page'] == 'old', 'time_spent_on_the_page'], alternative = 'greater')\n",
    "print('The p-value is ', p_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the p value is lesser than α (0.05), we REJECT the Null Hypothesis. Hence, we have enough statistical significance to conclude that users spend more time on the new landing page than the old landing page."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Is the conversion rate for the new page greater than the conversion rate for the old page?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hypothesis Formulation;\n",
    "\n",
    "Using the two independent sample t-test\n",
    "\n",
    "* $H_0: \\mu_{new} = \\mu_{old}$ (Conversion rate for the new page equals the conversion rate for the old page)\n",
    "\n",
    "* $H_a: \\mu_{new} > \\mu_{old}$ (Conversion rate for the new page is greater than the conversion rate for the old page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "\n",
    "sns.countplot(df[\"landing_page\"], hue=df['converted'], palette='PuBu');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The p-value is  0.4202884081666445\n"
     ]
    }
   ],
   "source": [
    "# Perform two independent sample t-test\n",
    "\n",
    "df_new = df.loc[df['landing_page'] == 'new', 'converted'][df['converted']=='yes'].value_counts()\n",
    "df_old = df.loc[df['landing_page'] == 'old', 'converted'][df['converted']=='yes'].value_counts()\n",
    "\n",
    "test_stat, p_value = ttest_ind(df_new, df_old, alternative = 'greater')\n",
    "print('The p-value is ', p_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the p value is greater than α (0.05), we fail to reject the null hypothesis. Hence, we don't have enough statistical significance to conclude that the conversion rate for the new page is greater than the conversion rate for the old page."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Does the converted status depend on the preferred language?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Null and Alternative Hypothesis\n",
    "\n",
    "We will test the null hypothesis\n",
    "\n",
    "$H_0:$ Converted status is independent of preferred language.\n",
    "\n",
    "against the alternate hypothesis\n",
    "\n",
    "$H_a:$ Converted status depends on the preferred language."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "language_preferred  English  French  Spanish\n",
      "converted                                   \n",
      "no                       12      17       16\n",
      "yes                      20      17       18\n"
     ]
    }
   ],
   "source": [
    "# Creating a contingency table\n",
    "\n",
    "contingency=pd.crosstab(df.converted, df.language_preferred) \n",
    "print(contingency)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The p-value is 0.5686624745121615\n"
     ]
    }
   ],
   "source": [
    "# Import the required function\n",
    "from scipy.stats import chi2_contingency\n",
    "\n",
    "# Find the p_value\n",
    "chi, p_value, dof, expected = chi2_contingency(contingency)\n",
    "print('The p-value is', p_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the p-value is greater than the significance level, we fail to reject the null hypothesis. Hence, we do have enough statistical significance to conclude that converted status is independent of preferred language at 5% significance level."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Is the mean time spent on the new page same for the different language users?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hypothesis Formulation;\n",
    "\n",
    "### Let's write the null and alternative hypothesis\n",
    "\n",
    "Let $\\mu_1, \\mu_2, \\mu_3$ be the mean time spent on the new page of English, French and Spanish, respectively.\n",
    "\n",
    "We will test the null hypothesis\n",
    "\n",
    ">$H_0: \\mu_1 = \\mu_2 = \\mu_3$\n",
    "\n",
    "against the alternative hypothesis\n",
    "\n",
    ">$H_a: $ At least the mean time spent on the new page for a language is different from the rest.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pxvFdeGcfs448ppJ+Pm7wyszfmsoGM/PBiPiviDg+M+8AXgn8x1S2IUmS1IrKPNV4dERcHhEbI+JnEXFZRBw9yXZXAl8t1oB8LvDxSZ5PkiSp5ZW51PhFGus2vrHYPqvYd8pEG83MmwCvg0iSpGmlzFONnZn5xcwcKj4uALyoLkmStI/KBK+HIuKsiOgoPs4CNjW7MEmSpHZTJnidDZwJPAg8AJxR7JMkSdI+KPNU4/3AaRXUIkmS1NZqWSRbkiRpOjJ4SZIkVaTMPF5PK7NPkiRJYysz4nXZXvZdOtWFSJIktbtRb66PiGcCJwDzImLFiLfmAgc1uzBJkqR2M9ZTjccDrwUOA143Yv9W4O1NrEmSJKktjRq8MvMK4IqIOCkzf1BhTZImoa+vj4GBAS69bG93CWikgYEBbrr55rrLaGl9fX3Mnj277jKktlFmrca7I+JPgcUjj89MJ1GVJEnaB2WC1xXA94B/BYabW07zDWx9kHvWnF93GS1t8NFNzH/SIWwbvKXuUlrawNYHYf7RdZfxczo7OxkYGOCM00+vu5SWd/fdd3PcccfVXUZLu/SyyxzxkqZQmeB1cGa+v+mVVGDRokV1l7Bf2DCwg4FHt3PUgjl1l9La5h9tn5Ik7ZMywevKiHh1Zv7/plfTZCtWrBj/INHd3U1/fz8rV66suxRNUF9fn/d4jaO/v5+5c+d6j9c4+vr6OOaYY+ouQ2obZYLXO4E/jYjHgceBADIz5za1MkkT4ihcOZs2bWL79u0sWLCg7lJa2jHHHGOfkqZQmUWyD62iEElTw5HdchzZlVSHcYNXRATwFuBpmfnRiHgKcFRmrml6dZIkjWLjwA4uvLOv7jJa2iODQxw6f4ibtz1SdyktbePADp5SUVtlLjWeC+wEXgF8FNgGfA54fhPrkiRpVF7+LGdowwa2PzrAgiO9T28sT6G6PlUmeL0gM58XET8CyMxHIuLAJtclSdKovKRejpfUW0+ZRbJ3REQHkAAR0UljBEySJEn7oEzw+gxwObAwIj4GXAd8vKlVSZIktaEyTzV+NSLWAa8sdr0hM29vblmSJEntp8w9XgAHA7suN7p2hCRJ0gSMe6kxIv4S+BJwOHAE8MWI+PNmFyZJktRuyox4vRk4MTMfA4iIvwFuBP6qmYVJkiS1mzI31/8EOGjE9izgP5tSjSRJUhsrM+I1CNwWEVfTuMfrFOC6iPgMQGb+YRPrkyRJahtlgtflxccuPc0pRZIkqb2VmU7iS7teR8STgKdk5i1NrUqSJKkNlXmqsSci5kbE4cDNNJ5q/FTzS5MkSWovZW6un5eZW4AVwBczcwnwy80tS5Ikqf2UCV4zI+Io4EzgyibXI0mS1LbKBK+PAKuBuzPzhxFxLHBXc8uSJElqP2Vurr8EuGTE9j3A6c0sSpIkqR2VGfGSJEnSFDB4SZIkVcTgJUmSVJEy83gtjIgvRMS3iu1nRcRvN780SZKk9lJmxOsCGk81PrnYvhN4V5PqkSRJaltlgtcRmXkxsBMgM4eA4aZWJUmS1IbKBK/tETEfSICIeCGwualVSZIktaFx5/EC3gN8A3h6RHwf6ATOaGpVkiRJbajMBKo3RsTLgOOBAO7IzB1Nr0ySJKnNjBu8IqIDeDWwuDj+1IggMz/V5NokSZLaSplLjd8EHgPWU9xgL0mSpH1XJngdnZnPnuqGi5G0tUBvZr52qs8vSZLUaso81fitiDi1CW2/E7i9CeeVJElqSWWC1/XA5RExEBFbImJrRGyZTKMRcTTwGuAfJ3MeSZKk/UmZS43/FzgJWJ+ZOUXt/h3wPuDQ0Q6IiHOAcwAWLlxIT0/PFDWt8fT39zM8POzPXG3Nfq7pwH7eesoEr7uAW6cqdEXEa4GNmbkuIpaNdlxmngecB9DV1ZXLlo16qKbY+vXr6e/vx5+52pn9XNOB/bz1lAleDwA9xSLZg7t2TmI6iRcDp0XEq4GDgLkR8ZXMPGuC55MkSdovlAle9xYfBxYfk5KZfwL8CUAx4vVeQ5ckaX+3atUqent76y5jNxs2bGBoaIju7u66S9nNokWLWLFiRd1l1KLMzPUfrqIQSZI0tWbNmlV3CdrDqMErIj6bme+IiG9SLJA9UmaeNtnGM7MH6JnseSRJqlurjuD09PR4j1cLGWvE6zeAdwCfrKgWSZKktjZW8PpPgMy8pqJaJEmS2tpYwaszIt4z2psuki1JkrRvxgpeHcAhQFRUy7TkUzDlTeenYCRJ7WGs4PVAZn6kskrUMnwKRpKk5hgreDnSVYFWHcHxKRhJkqbeWItkv7KyKiRJkqaBUYNXZj5cZSGSJEntbqwRL0mSJE0hg5ckSVJFDF6SJEkVMXhJkiRVZKzpJCRpSjhRcHlOFCy1N4OXpGnJiYIl1cHgJanpWnUEx4mCJVXNe7wkSZIqYvCSJEmqiMFLkiSpIgYvSZKkihi8JEmSKmLwkiRJqojBS5IkqSIGL0mSpIoYvCRJkipi8JIkSaqIwUuSJKkiBi9JkqSKGLwkSZIqYvCSJEmqiMFLkiSpIgYvSZKkihi8JEmSKmLwkiRJqojBS5IkqSIGL0mSpIoYvCRJkipi8JIkSaqIwUuSJKkiBi9JkqSKGLwkSZIqYvCSJEmqiMFLkiSpIgYvSZKkihi8JEmSKmLwkiRJqkjlwSsinhIR342I2yPitoh4Z9U1SJIk1WFmDW0OAX+UmTdGxKHAuoi4OjP/o4ZaJEmSKlP5iFdmPpCZNxavtwK3A4uqrkOSJKlqtd7jFRGLgROBG+qsQ5IkqQp1XGoEICIOAS4D3pWZW/by/jnAOQALFy6kp6en2gKnuW3btvkzV9uzn2s6sJ+3lsjM6huNOAC4ElidmZ8a7/iurq5cu3Zt8wvT/+jp6WHZsmV1lyE1lf1c04H9vHoRsS4zu/b2Xh1PNQbwBeD2MqFLkiSpXdRxj9eLgbcCr4iIm4qPV9dQhyRJUqUqv8crM68Doup2JUmS6ubM9ZIktanNmzdz7bXXsmXLzz3DppoYvCRJalOrV69m06ZNXHXVVXWXooLBS5KkNrR582bWrFkDwJo1axz1ahEGL0mS2tDq1avZuXMnADt37nTUq0UYvCRJakPr1q1jeHgYgOHhYdatW1dzRQKDlyRJbWnJkiV0dHQA0NHRwZIlS2quSGDwkiSpLS1fvpwZMxr/m58xYwavetWraq5IYPCSJKktzZs3j6VLlwKwdOlS5s6dW3NFAoOXJElta/ny5cyfP9/RrhZi8JIkqU3NmzePk08+2dGuFmLwkiRJqojBS5IkqSIGL0mSpIoYvCRJkipi8JIkSaqIwUuSJKkiBi9JkqSKRGbWXcO4IqIPuK/uOqaZI4CH6i5CajL7uaYD+3n1npqZnXt7Y78IXqpeRKzNzK6665CayX6u6cB+3lq81ChJklQRg5ckSVJFDF4azXl1FyBVwH6u6cB+3kK8x0uSJKkijnhJkiRVxODVhiJiOCJuGvHxgUmca1vx+ckRcekYxy2OiFsn2o40EXvp64ub1M6yiLiyGeeWRhMRfxYRt0XELUX/fsEUn//fx3l/21S2p4aZdRegphjIzOdO5Qkz86fAGVN5TmkKjNrXIyJo3E6xs9qSpMmLiJOA1wLPy8zBiDgCOHAq28jMF03l+VSOI17TSET8JCI+HBE3RsT6iHhmsb8zIq4u9n8+Iu4rfslHfu3/jGhFxAkRsab4F9gtEfGM4rCOiPiH4l9o346I2RV/i5rmin56e0ScC9wIPCUi/jgiflj01Q/vcdzP9deIOC4i/jUibi5+J55enP6QiLg0In4cEV8tgp3ULEcBD2XmIEBmPpSZPy3+jn+i+Bu8JiKOA4iI10XEDRHxo6L/Liz2fygizo+Inoi4JyL+cFcDI65oHBUR1xZ/02+NiJeOOOZjxe/C9bvOqckxeLWn2XtcfnnTiPceysznAX8PvLfY90Hg34r9lwPHjHP+3wU+XYw0dAEbiv3PAD6XmScA/cDpU/LdSKMb2dcvL/YdD/xTZp5YvH4GsBR4LrAkIk4ujhutv3612P8c4EXAA8X+E4F3Ac8CjgVe3MTvS/o2jX843BkR50bEy0a8tyUzlwKfBf6u2Hcd8MKi338NeN+I458JLKfxe/DBiDhgj7Z+HVhd/E1/DnBTsX8OcH3xu3At8PYp+t6mNS81tqexLjWuKj6vA1YUr18C/CpAZl4VEY+Mc/4fAH8WEUcDqzLzruIf//dm5k0jzr94QtVL5e3W14t7vO7LzOuLXacWHz8qtg+hEbjuZy/9NSIOBRZl5uUAmflYcV6ANZm5odi+iUb/vq4535amu8zcFhFLgJcCLwf+ecT9uheN+Pz/itdHF8ccReOS5L0jTvcvxcjZYERsBBbyxD+YAX4InF8Esq+P+L14HNh1b+M64JSp+v6mM0e8pp/B4vMwTwTvfbpkkpkXAqcBA8DqiHjFHufe8/xSlbaPeB3AX2fmc4uP4zLzC8V7e+uvY/0u2L9VqcwczsyezPwg8A6eGJUdOQ/UrtfdwGcz85eA3wEOGnHMmH03M68FTgZ6gS9HxG8Ub+3IJ+acss9PEYOXoPGv9jMBIuJU4EljHRwRxwL3ZOZngG8Az256hdLErAbOjohDACJiUUQsGO3gzNwCbIiINxTHz4qIgyupVBohIo4fcf8sNC6V31e8ftOIzz8oXs+jEZwA3raPbT0V2JiZ/wB8AXjeRGpWOabX9jS7uBSyy1WZOdaUEh8GLiruBbuGxj0tW8c4/k3AWRGxA3gQ+Agwd3IlS1MvM78dEf8L+EFxuXAbcBaNf72P5q3A5yPiI8AO4I1NL1T6eYcA3RFxGDAE3A2cQ+NJx1kRcQONwZM3F8d/CLgkInqB64Gn7UNby4A/Lv6mbwN+Y+zDNRnOXC8iYhYwnJlDxSPMfz/V01FIkiYvIn4CdGXmQ3XXoolxxEvQeIrx4oiYQeNmSp9ckSSpCRzxkiRJqog310uSJFXE4CVJklQRg5ckSVJFDF6SJmzXWm96QkRcVKwL+e4K2vLnL+1nfKpRkvZBRMzMzKFR3jsSeFFmPnWi5xvr/JL2fwYvSVMqIl4H/DmN9eI2AW/JzJ9FxIdoTF1ybPH574rVD4iIvwDeAvwX8BCwLjM/GRE9wHszc21EHAGszczFxZqMX6axiC/AOzLz34spUT4LvIzGWnUzgPMz89Ji3btP0ZiY8iHgNzNz1wLYu2q/AHgMOIHGenbvycwrI+I3gdfQWIZlTvE9dgO/ROPv6Icy8woaCxsvKCYwXgn8FPgc0Ak8Crw9M39ctPMwjYW3b4yI+XtsnzvK1z0NuLBo86p9/o8jqXYGL0lT7TrghZmZEfG/gfcBf1S890waC/4eCtwREX8PPIfGGnQn0vibdCONBXnHshE4JTMfK5ZVuQjoorHw+2IagWgBcDtPLP7bDbw+M/uKVRo+Bpy9l3MvphHcng58NyKOK/afBDw7Mx+OiI8D/5aZZxczi6+JiH+lsYbplbsmII6I7wC/Wywk/wLgXGDX2qa/APxyZg4XQWzk9mhf92kaExz/U0T8wTg/I0ktyOAlaaodDfxzRBxFY9Tr3hHv/UtmDgKDEbGRxqjSS4ArMnMAICK+WaKNA4DPRsRzaSz/8wvF/pcAl2TmTuDBiPhusf944BeBq4ulgzpoLI21NxcXX39XRNxDIywCXJ2ZDxevTwVOi4j3FtsH0RjFG9h1kmJ9yBfRWMZl1+5ZI9q5JDOH99we5+tezBMLJX8Z+MQo34OkFmXwkjTVuoFPZeY3ImIZjTXkdhkc8XqYxt+gYHRDPPEQ0EEj9r8b+BmN0bIZNC4PMsa5ArgtM08av3z2nFV61/b2Pc53embesVsjjUugu8wA+sdYfmv7KNvjfZ2zXkv7MZ9qlDTV5gG9xeu3lTj+OuB1EXFQMdrzmhHv/QRYUrw+Y482HihGpt5KYwRr17lOj4gZEbGQxuK/AHcAncVapETEARFxwij1vLH4+qfTuB/tjr0csxpYGcWQVEScuOcBmbkFuDci3lgcExHxnNF+CCW/7vvArxWv3zLeuSS1HoOXpMk4OCI2jPh4D40Rrksi4ns0bmIfU2b+EPgGcDOwClgLbC7e/iTwexHx78ARI77sXOBtEXE9jcuMu0aLLgM2ALcCnwduADZn5uM0gtsnIuJm4CYal/P25g7gGuBbNO6zemwvx3yUxuXOWyLi1mJ7b94C/HbR5m3A60c5ruzXvRP4g4j4IY3wKWk/41qNkmoXEYdk5raIOBi4FjgnM2+c5LnmA2uAF2fmgyW/9gIaN8dfOpG2JWk83uMlqRWcFxHPonEf15cmGroKVxZPGh4IfLRs6JKkKjjiJUmSVBHv8ZIkSaqIwUuSJKkiBi9JkqSKGLwkSZIqYvCSJEmqiMFLkiSpIv8NHYRRw3yvH50AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "\n",
    "sns.boxplot(x = df.loc[df['landing_page'] == 'new', 'language_preferred'], \n",
    "            y = df.loc[df['landing_page'] == 'new', 'time_spent_on_the_page'], palette='coolwarm')\n",
    "\n",
    "plt.xlabel('Language preferred')\n",
    "plt.ylabel('Time spent on the new page')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The p-value is 0.43204138694325955\n"
     ]
    }
   ],
   "source": [
    "# perform one-way anova test\n",
    "\n",
    "mean_time_english = df.loc[df['language_preferred'] == 'English', 'time_spent_on_the_page'][df['landing_page']=='new']\n",
    "mean_time_french = df.loc[df['language_preferred'] == 'French', 'time_spent_on_the_page'][df['landing_page']=='new']\n",
    "mean_time_spanish = df.loc[df['language_preferred'] == 'Spanish', 'time_spent_on_the_page'][df['landing_page']=='new']\n",
    "\n",
    "\n",
    "test_stat, p_value = stats.f_oneway(mean_time_english, mean_time_french, mean_time_spanish)\n",
    "\n",
    "print('The p-value is', p_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Insight\n",
    "As the p-value is greater than the significance level (0.05), we fail to reject the null hypothesis. Hence, we have enough statistical significance to conclude that the means of the time spent on the new page is same for the different language users."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Users who got converted in both groups spend more time one the page\n",
    "* The treatment group landing on the new page spend more time on the page compared to the control group.\n",
    "* Users with English as preferred language spend the most time on the new page and users with Spanish as preferred language spend the most time on the old page.\n",
    "* Conversion rate for the new page is greater than the conversion rate for the old page.\n",
    "* Users with English as preferred language have the highest conversion rate.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Recommendation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The company should utilize the new landing page more as it proves its effectiveness in gathering new subscribers  because users who landed on the new page spend more time on the page and it has an higher conversion rate.\n",
    "* The company needs to engage in more new features on the new landing page to attract more users to get converted."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
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