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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Lab | Hypothesis Testing"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Objective**\n",
+    "\n",
+    "Welcome to the Hypothesis Testing Lab, where we embark on an enlightening journey through the realm of statistical decision-making! In this laboratory, we delve into various scenarios, applying the powerful tools of hypothesis testing to scrutinize and interpret data.\n",
+    "\n",
+    "From testing the mean of a single sample (One Sample T-Test), to investigating differences between independent groups (Two Sample T-Test), and exploring relationships within dependent samples (Paired Sample T-Test), our exploration knows no bounds. Furthermore, we'll venture into the realm of Analysis of Variance (ANOVA), unraveling the complexities of comparing means across multiple groups.\n",
+    "\n",
+    "So, grab your statistical tools, prepare your hypotheses, and let's embark on this fascinating journey of exploration and discovery in the world of hypothesis testing!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Challenge 1**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this challenge, we will be working with pokemon data. The data can be found here:\n",
+    "\n",
+    "- https://raw.githubusercontent.com/data-bootcamp-v4/data/main/pokemon.csv"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#libraries\n",
+    "import pandas as pd\n",
+    "import scipy.stats as st\n",
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Name</th>\n",
+       "      <th>Type 1</th>\n",
+       "      <th>Type 2</th>\n",
+       "      <th>HP</th>\n",
+       "      <th>Attack</th>\n",
+       "      <th>Defense</th>\n",
+       "      <th>Sp. Atk</th>\n",
+       "      <th>Sp. Def</th>\n",
+       "      <th>Speed</th>\n",
+       "      <th>Generation</th>\n",
+       "      <th>Legendary</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>Bulbasaur</td>\n",
+       "      <td>Grass</td>\n",
+       "      <td>Poison</td>\n",
+       "      <td>45</td>\n",
+       "      <td>49</td>\n",
+       "      <td>49</td>\n",
+       "      <td>65</td>\n",
+       "      <td>65</td>\n",
+       "      <td>45</td>\n",
+       "      <td>1</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>Ivysaur</td>\n",
+       "      <td>Grass</td>\n",
+       "      <td>Poison</td>\n",
+       "      <td>60</td>\n",
+       "      <td>62</td>\n",
+       "      <td>63</td>\n",
+       "      <td>80</td>\n",
+       "      <td>80</td>\n",
+       "      <td>60</td>\n",
+       "      <td>1</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>Venusaur</td>\n",
+       "      <td>Grass</td>\n",
+       "      <td>Poison</td>\n",
+       "      <td>80</td>\n",
+       "      <td>82</td>\n",
+       "      <td>83</td>\n",
+       "      <td>100</td>\n",
+       "      <td>100</td>\n",
+       "      <td>80</td>\n",
+       "      <td>1</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>Mega Venusaur</td>\n",
+       "      <td>Grass</td>\n",
+       "      <td>Poison</td>\n",
+       "      <td>80</td>\n",
+       "      <td>100</td>\n",
+       "      <td>123</td>\n",
+       "      <td>122</td>\n",
+       "      <td>120</td>\n",
+       "      <td>80</td>\n",
+       "      <td>1</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>Charmander</td>\n",
+       "      <td>Fire</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>39</td>\n",
+       "      <td>52</td>\n",
+       "      <td>43</td>\n",
+       "      <td>60</td>\n",
+       "      <td>50</td>\n",
+       "      <td>65</td>\n",
+       "      <td>1</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>...</th>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "      <td>...</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>795</th>\n",
+       "      <td>Diancie</td>\n",
+       "      <td>Rock</td>\n",
+       "      <td>Fairy</td>\n",
+       "      <td>50</td>\n",
+       "      <td>100</td>\n",
+       "      <td>150</td>\n",
+       "      <td>100</td>\n",
+       "      <td>150</td>\n",
+       "      <td>50</td>\n",
+       "      <td>6</td>\n",
+       "      <td>True</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>796</th>\n",
+       "      <td>Mega Diancie</td>\n",
+       "      <td>Rock</td>\n",
+       "      <td>Fairy</td>\n",
+       "      <td>50</td>\n",
+       "      <td>160</td>\n",
+       "      <td>110</td>\n",
+       "      <td>160</td>\n",
+       "      <td>110</td>\n",
+       "      <td>110</td>\n",
+       "      <td>6</td>\n",
+       "      <td>True</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>797</th>\n",
+       "      <td>Hoopa Confined</td>\n",
+       "      <td>Psychic</td>\n",
+       "      <td>Ghost</td>\n",
+       "      <td>80</td>\n",
+       "      <td>110</td>\n",
+       "      <td>60</td>\n",
+       "      <td>150</td>\n",
+       "      <td>130</td>\n",
+       "      <td>70</td>\n",
+       "      <td>6</td>\n",
+       "      <td>True</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>798</th>\n",
+       "      <td>Hoopa Unbound</td>\n",
+       "      <td>Psychic</td>\n",
+       "      <td>Dark</td>\n",
+       "      <td>80</td>\n",
+       "      <td>160</td>\n",
+       "      <td>60</td>\n",
+       "      <td>170</td>\n",
+       "      <td>130</td>\n",
+       "      <td>80</td>\n",
+       "      <td>6</td>\n",
+       "      <td>True</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>799</th>\n",
+       "      <td>Volcanion</td>\n",
+       "      <td>Fire</td>\n",
+       "      <td>Water</td>\n",
+       "      <td>80</td>\n",
+       "      <td>110</td>\n",
+       "      <td>120</td>\n",
+       "      <td>130</td>\n",
+       "      <td>90</td>\n",
+       "      <td>70</td>\n",
+       "      <td>6</td>\n",
+       "      <td>True</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>800 rows × 11 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "               Name   Type 1  Type 2  HP  Attack  Defense  Sp. Atk  Sp. Def  \\\n",
+       "0         Bulbasaur    Grass  Poison  45      49       49       65       65   \n",
+       "1           Ivysaur    Grass  Poison  60      62       63       80       80   \n",
+       "2          Venusaur    Grass  Poison  80      82       83      100      100   \n",
+       "3     Mega Venusaur    Grass  Poison  80     100      123      122      120   \n",
+       "4        Charmander     Fire     NaN  39      52       43       60       50   \n",
+       "..              ...      ...     ...  ..     ...      ...      ...      ...   \n",
+       "795         Diancie     Rock   Fairy  50     100      150      100      150   \n",
+       "796    Mega Diancie     Rock   Fairy  50     160      110      160      110   \n",
+       "797  Hoopa Confined  Psychic   Ghost  80     110       60      150      130   \n",
+       "798   Hoopa Unbound  Psychic    Dark  80     160       60      170      130   \n",
+       "799       Volcanion     Fire   Water  80     110      120      130       90   \n",
+       "\n",
+       "     Speed  Generation  Legendary  \n",
+       "0       45           1      False  \n",
+       "1       60           1      False  \n",
+       "2       80           1      False  \n",
+       "3       80           1      False  \n",
+       "4       65           1      False  \n",
+       "..     ...         ...        ...  \n",
+       "795     50           6       True  \n",
+       "796    110           6       True  \n",
+       "797     70           6       True  \n",
+       "798     80           6       True  \n",
+       "799     70           6       True  \n",
+       "\n",
+       "[800 rows x 11 columns]"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df = pd.read_csv(\"https://raw.githubusercontent.com/data-bootcamp-v4/data/main/pokemon.csv\")\n",
+    "df"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array(['Grass', 'Fire', 'Water', 'Bug', 'Normal', 'Poison', 'Electric',\n",
+       "       'Ground', 'Fairy', 'Fighting', 'Psychic', 'Rock', 'Ghost', 'Ice',\n",
+       "       'Dragon', 'Dark', 'Steel', 'Flying'], dtype=object)"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df[\"Type 1\"].unique()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array(['Poison', nan, 'Flying', 'Dragon', 'Ground', 'Fairy', 'Grass',\n",
+       "       'Fighting', 'Psychic', 'Steel', 'Ice', 'Rock', 'Dark', 'Water',\n",
+       "       'Electric', 'Fire', 'Ghost', 'Bug', 'Normal'], dtype=object)"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df[\"Type 2\"].unique()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Name</th>\n",
+       "      <th>Type 1</th>\n",
+       "      <th>Type 2</th>\n",
+       "      <th>HP</th>\n",
+       "      <th>Attack</th>\n",
+       "      <th>Defense</th>\n",
+       "      <th>Sp. Atk</th>\n",
+       "      <th>Sp. Def</th>\n",
+       "      <th>Speed</th>\n",
+       "      <th>Generation</th>\n",
+       "      <th>Legendary</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>275</th>\n",
+       "      <td>Mega Sceptile</td>\n",
+       "      <td>Grass</td>\n",
+       "      <td>Dragon</td>\n",
+       "      <td>70</td>\n",
+       "      <td>110</td>\n",
+       "      <td>75</td>\n",
+       "      <td>145</td>\n",
+       "      <td>85</td>\n",
+       "      <td>145</td>\n",
+       "      <td>3</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "              Name Type 1  Type 2  HP  Attack  Defense  Sp. Atk  Sp. Def  \\\n",
+       "275  Mega Sceptile  Grass  Dragon  70     110       75      145       85   \n",
+       "\n",
+       "     Speed  Generation  Legendary  \n",
+       "275    145           3      False  "
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "both_types = df[(\n",
+    "        (df[\"Type 1\"] == \"Dragon\") |\n",
+    "        (df[\"Type 2\"] == \"Dragon\"))\n",
+    "    &\n",
+    "    ((df[\"Type 1\"] == \"Grass\") |\n",
+    "    (df[\"Type 2\"] == \"Grass\")\n",
+    ")]\n",
+    "\n",
+    "both_types"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Index([275], dtype='int64')"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "overlap_pokemon = both_types.index\n",
+    "overlap_pokemon"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "- We posit that Pokemons of type Dragon have, on average, more HP stats than Grass. Choose the proper test and, with 5% significance, comment your findings."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# H0: dragon_mean_hp <= grass_mean_hp\n",
+    "# H1: dragon__mean_hp > grass_mean_hp\n",
+    "\n",
+    "alpha = 0.05 #significance level"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "7       78\n",
+      "159     41\n",
+      "160     61\n",
+      "161     91\n",
+      "196     90\n",
+      "249     75\n",
+      "360     50\n",
+      "361     80\n",
+      "365     75\n",
+      "366     75\n",
+      "406     45\n",
+      "407     65\n",
+      "408     95\n",
+      "409     95\n",
+      "417     80\n",
+      "418     80\n",
+      "419     80\n",
+      "420     80\n",
+      "425    105\n",
+      "426    105\n",
+      "491     58\n",
+      "492     68\n",
+      "493    108\n",
+      "494    108\n",
+      "540    100\n",
+      "541     90\n",
+      "544    150\n",
+      "545    150\n",
+      "671     46\n",
+      "672     66\n",
+      "673     76\n",
+      "682     77\n",
+      "694     52\n",
+      "695     72\n",
+      "696     92\n",
+      "706    100\n",
+      "707    100\n",
+      "710    125\n",
+      "711    125\n",
+      "712    125\n",
+      "761     65\n",
+      "766     58\n",
+      "767     82\n",
+      "774     45\n",
+      "775     68\n",
+      "776     90\n",
+      "790     40\n",
+      "791     85\n",
+      "794    108\n",
+      "Name: HP, dtype: int64\n",
+      "0      45\n",
+      "1      60\n",
+      "2      80\n",
+      "3      80\n",
+      "48     45\n",
+      "       ..\n",
+      "783    59\n",
+      "784    65\n",
+      "785    55\n",
+      "786    75\n",
+      "787    85\n",
+      "Name: HP, Length: 94, dtype: int64\n"
+     ]
+    }
+   ],
+   "source": [
+    "dragon_hp = df[((df[\"Type 1\"] == \"Dragon\") | (df[\"Type 2\"] == \"Dragon\")) & (~df.index.isin(overlap_pokemon))][\"HP\"]\n",
+    "grass_hp = df[((df[\"Type 1\"] == \"Grass\") | (df[\"Type 2\"] == \"Grass\")) & (~df.index.isin(overlap_pokemon))][\"HP\"]\n",
+    "print(dragon_hp)\n",
+    "print(grass_hp)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "np.float64(83.16326530612245)"
+      ]
+     },
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dragon_hp.mean()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "np.float64(66.01063829787235)"
+      ]
+     },
+     "execution_count": 32,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "grass_hp.mean()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "5.060530308690885e-05\n"
+     ]
+    }
+   ],
+   "source": [
+    "p_value = st.ttest_ind(dragon_hp, grass_hp, equal_var=False, alternative = \"greater\").pvalue\n",
+    "print(p_value)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H0 can be rejected\n"
+     ]
+    }
+   ],
+   "source": [
+    "#Decision-making\n",
+    "if p_value < alpha:\n",
+    "    print(\"H0 can be rejected\")\n",
+    "else:\n",
+    "    print(\"Fail to reject H0\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "- Since the H0 was rejected, pokemon of the dragon type have statistically significant higher average HP than grass types."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "- We posit that Legendary Pokemons have different stats (HP, Attack, Defense, Sp.Atk, Sp.Def, Speed) when comparing with Non-Legendary. Choose the propper test and, with 5% significance, comment your findings.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# H0: lengendary_pokemons = non-legendary_pokemons\n",
+    "# H1: lengendary_pokemons != non-legendary_pokemons\n",
+    "alpha = 0.05"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "HP\n",
+      "P-value: 0.00000\n",
+      "Reject H0\n",
+      "\n",
+      "Attack\n",
+      "P-value: 0.00000\n",
+      "Reject H0\n",
+      "\n",
+      "Defense\n",
+      "P-value: 0.00000\n",
+      "Reject H0\n",
+      "\n",
+      "Sp. Atk\n",
+      "P-value: 0.00000\n",
+      "Reject H0\n",
+      "\n",
+      "Sp. Def\n",
+      "P-value: 0.00000\n",
+      "Reject H0\n",
+      "\n",
+      "Speed\n",
+      "P-value: 0.00000\n",
+      "Reject H0\n"
+     ]
+    }
+   ],
+   "source": [
+    "stats = [\"HP\", \"Attack\", \"Defense\", \"Sp. Atk\", \"Sp. Def\", \"Speed\"]\n",
+    "        \n",
+    "legendary = df[df[\"Legendary\"] == True]\n",
+    "non_legendary = df[df[\"Legendary\"] == False]\n",
+    "\n",
+    "for stat in stats:\n",
+    "    p_value = st.ttest_ind(\n",
+    "        legendary[stat],\n",
+    "        non_legendary[stat],\n",
+    "        equal_var=False).pvalue\n",
+    "\n",
+    "    print(f\"\\n{stat}\")\n",
+    "    print(f\"P-value: {p_value:.5f}\")\n",
+    "\n",
+    "    if p_value < alpha:\n",
+    "        print(\"Reject H0\")\n",
+    "    else:\n",
+    "        print(\"Fail to reject H0\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "- At the 5% significance level, the p-value for all statistics  is less than 0.05. Therefore, we reject the H0 for all six stats. So, there is sufficient statistical evidence that legendary and non-legendary pokemons differ significantly in each of the selected stats."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Challenge 2**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this challenge, we will be working with california-housing data. The data can be found here:\n",
+    "- https://raw.githubusercontent.com/data-bootcamp-v4/data/main/california_housing.csv"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>longitude</th>\n",
+       "      <th>latitude</th>\n",
+       "      <th>housing_median_age</th>\n",
+       "      <th>total_rooms</th>\n",
+       "      <th>total_bedrooms</th>\n",
+       "      <th>population</th>\n",
+       "      <th>households</th>\n",
+       "      <th>median_income</th>\n",
+       "      <th>median_house_value</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>-114.31</td>\n",
+       "      <td>34.19</td>\n",
+       "      <td>15.0</td>\n",
+       "      <td>5612.0</td>\n",
+       "      <td>1283.0</td>\n",
+       "      <td>1015.0</td>\n",
+       "      <td>472.0</td>\n",
+       "      <td>1.4936</td>\n",
+       "      <td>66900.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>-114.47</td>\n",
+       "      <td>34.40</td>\n",
+       "      <td>19.0</td>\n",
+       "      <td>7650.0</td>\n",
+       "      <td>1901.0</td>\n",
+       "      <td>1129.0</td>\n",
+       "      <td>463.0</td>\n",
+       "      <td>1.8200</td>\n",
+       "      <td>80100.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>-114.56</td>\n",
+       "      <td>33.69</td>\n",
+       "      <td>17.0</td>\n",
+       "      <td>720.0</td>\n",
+       "      <td>174.0</td>\n",
+       "      <td>333.0</td>\n",
+       "      <td>117.0</td>\n",
+       "      <td>1.6509</td>\n",
+       "      <td>85700.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>-114.57</td>\n",
+       "      <td>33.64</td>\n",
+       "      <td>14.0</td>\n",
+       "      <td>1501.0</td>\n",
+       "      <td>337.0</td>\n",
+       "      <td>515.0</td>\n",
+       "      <td>226.0</td>\n",
+       "      <td>3.1917</td>\n",
+       "      <td>73400.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>-114.57</td>\n",
+       "      <td>33.57</td>\n",
+       "      <td>20.0</td>\n",
+       "      <td>1454.0</td>\n",
+       "      <td>326.0</td>\n",
+       "      <td>624.0</td>\n",
+       "      <td>262.0</td>\n",
+       "      <td>1.9250</td>\n",
+       "      <td>65500.0</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   longitude  latitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
+       "0    -114.31     34.19                15.0       5612.0          1283.0   \n",
+       "1    -114.47     34.40                19.0       7650.0          1901.0   \n",
+       "2    -114.56     33.69                17.0        720.0           174.0   \n",
+       "3    -114.57     33.64                14.0       1501.0           337.0   \n",
+       "4    -114.57     33.57                20.0       1454.0           326.0   \n",
+       "\n",
+       "   population  households  median_income  median_house_value  \n",
+       "0      1015.0       472.0         1.4936             66900.0  \n",
+       "1      1129.0       463.0         1.8200             80100.0  \n",
+       "2       333.0       117.0         1.6509             85700.0  \n",
+       "3       515.0       226.0         3.1917             73400.0  \n",
+       "4       624.0       262.0         1.9250             65500.0  "
+      ]
+     },
+     "execution_count": 48,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df = pd.read_csv(\"https://raw.githubusercontent.com/data-bootcamp-v4/data/main/california_housing.csv\")\n",
+    "df.head()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**We posit that houses close to either a school or a hospital are more expensive.**\n",
+    "\n",
+    "- School coordinates (-118, 34)\n",
+    "- Hospital coordinates (-122, 37)\n",
+    "\n",
+    "We consider a house (neighborhood) to be close to a school or hospital if the distance is lower than 0.50.\n",
+    "\n",
+    "Hint:\n",
+    "- Write a function to calculate euclidean distance from each house (neighborhood) to the school and to the hospital.\n",
+    "- Divide your dataset into houses close and far from either a hospital or school.\n",
+    "- Choose the propper test and, with 5% significance, comment your findings.\n",
+    " "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# H0: house_close <= house_far\n",
+    "# H1: house_close > house_far\n",
+    "\n",
+    "def euclidean_distance(x1, y1, x2, y2):\n",
+    "    return np.sqrt((x2 - x1)**2 + (y2 - y1)**2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df[\"distance_school\"] = euclidean_distance(\n",
+    "    df[\"longitude\"],\n",
+    "    df[\"latitude\"],\n",
+    "    -118,\n",
+    "    34\n",
+    ")\n",
+    "\n",
+    "df[\"distance_hospital\"] = euclidean_distance(\n",
+    "    df[\"longitude\"],\n",
+    "    df[\"latitude\"],\n",
+    "    -122,\n",
+    "    37\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>longitude</th>\n",
+       "      <th>latitude</th>\n",
+       "      <th>housing_median_age</th>\n",
+       "      <th>total_rooms</th>\n",
+       "      <th>total_bedrooms</th>\n",
+       "      <th>population</th>\n",
+       "      <th>households</th>\n",
+       "      <th>median_income</th>\n",
+       "      <th>median_house_value</th>\n",
+       "      <th>distance_school</th>\n",
+       "      <th>distance_hospital</th>\n",
+       "      <th>close</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>-114.31</td>\n",
+       "      <td>34.19</td>\n",
+       "      <td>15.0</td>\n",
+       "      <td>5612.0</td>\n",
+       "      <td>1283.0</td>\n",
+       "      <td>1015.0</td>\n",
+       "      <td>472.0</td>\n",
+       "      <td>1.4936</td>\n",
+       "      <td>66900.0</td>\n",
+       "      <td>3.694888</td>\n",
+       "      <td>8.187319</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>-114.47</td>\n",
+       "      <td>34.40</td>\n",
+       "      <td>19.0</td>\n",
+       "      <td>7650.0</td>\n",
+       "      <td>1901.0</td>\n",
+       "      <td>1129.0</td>\n",
+       "      <td>463.0</td>\n",
+       "      <td>1.8200</td>\n",
+       "      <td>80100.0</td>\n",
+       "      <td>3.552591</td>\n",
+       "      <td>7.966235</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>-114.56</td>\n",
+       "      <td>33.69</td>\n",
+       "      <td>17.0</td>\n",
+       "      <td>720.0</td>\n",
+       "      <td>174.0</td>\n",
+       "      <td>333.0</td>\n",
+       "      <td>117.0</td>\n",
+       "      <td>1.6509</td>\n",
+       "      <td>85700.0</td>\n",
+       "      <td>3.453940</td>\n",
+       "      <td>8.143077</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>-114.57</td>\n",
+       "      <td>33.64</td>\n",
+       "      <td>14.0</td>\n",
+       "      <td>1501.0</td>\n",
+       "      <td>337.0</td>\n",
+       "      <td>515.0</td>\n",
+       "      <td>226.0</td>\n",
+       "      <td>3.1917</td>\n",
+       "      <td>73400.0</td>\n",
+       "      <td>3.448840</td>\n",
+       "      <td>8.154416</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>-114.57</td>\n",
+       "      <td>33.57</td>\n",
+       "      <td>20.0</td>\n",
+       "      <td>1454.0</td>\n",
+       "      <td>326.0</td>\n",
+       "      <td>624.0</td>\n",
+       "      <td>262.0</td>\n",
+       "      <td>1.9250</td>\n",
+       "      <td>65500.0</td>\n",
+       "      <td>3.456848</td>\n",
+       "      <td>8.183508</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   longitude  latitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
+       "0    -114.31     34.19                15.0       5612.0          1283.0   \n",
+       "1    -114.47     34.40                19.0       7650.0          1901.0   \n",
+       "2    -114.56     33.69                17.0        720.0           174.0   \n",
+       "3    -114.57     33.64                14.0       1501.0           337.0   \n",
+       "4    -114.57     33.57                20.0       1454.0           326.0   \n",
+       "\n",
+       "   population  households  median_income  median_house_value  distance_school  \\\n",
+       "0      1015.0       472.0         1.4936             66900.0         3.694888   \n",
+       "1      1129.0       463.0         1.8200             80100.0         3.552591   \n",
+       "2       333.0       117.0         1.6509             85700.0         3.453940   \n",
+       "3       515.0       226.0         3.1917             73400.0         3.448840   \n",
+       "4       624.0       262.0         1.9250             65500.0         3.456848   \n",
+       "\n",
+       "   distance_hospital  close  \n",
+       "0           8.187319  False  \n",
+       "1           7.966235  False  \n",
+       "2           8.143077  False  \n",
+       "3           8.154416  False  \n",
+       "4           8.183508  False  "
+      ]
+     },
+     "execution_count": 55,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df[\"close\"] = ((df[\"distance_school\"] < 0.5) | (df[\"distance_hospital\"] < 0.5))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 56,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "close_houses = df[df[\"close\"]][\"median_house_value\"]\n",
+    "far_houses = df[~df[\"close\"]][\"median_house_value\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1.5032478884296307e-301\n"
+     ]
+    }
+   ],
+   "source": [
+    "p_value = st.ttest_ind(\n",
+    "    close_houses,\n",
+    "    far_houses,\n",
+    "    equal_var=False,\n",
+    "    alternative=\"greater\").pvalue\n",
+    "\n",
+    "print(p_value)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Reject H0\n"
+     ]
+    }
+   ],
+   "source": [
+    "alpha = 0.05\n",
+    "\n",
+    "if p_value < alpha:\n",
+    "    print(\"Reject H0\")\n",
+    "else:\n",
+    "    print(\"Fail to reject H0\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "- There is sufficient statistical evidence to conclude that houses located within 0.50 units of either a school or a hospital have a higher mean house value than houses located farther away."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.13.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/lab-hypothesis-testing.ipynb b/lab-hypothesis-testing.ipynb
index 0cc26d5..d951be6 100644
--- a/lab-hypothesis-testing.ipynb
+++ b/lab-hypothesis-testing.ipynb
@@ -45,13 +45,12 @@
     "#libraries\n",
     "import pandas as pd\n",
     "import scipy.stats as st\n",
-    "import numpy as np\n",
-    "\n"
+    "import numpy as np"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
@@ -278,7 +277,7 @@
        "[800 rows x 11 columns]"
       ]
      },
-     "execution_count": 3,
+     "execution_count": 2,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -288,20 +287,340 @@
     "df"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array(['Grass', 'Fire', 'Water', 'Bug', 'Normal', 'Poison', 'Electric',\n",
+       "       'Ground', 'Fairy', 'Fighting', 'Psychic', 'Rock', 'Ghost', 'Ice',\n",
+       "       'Dragon', 'Dark', 'Steel', 'Flying'], dtype=object)"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df[\"Type 1\"].unique()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array(['Poison', nan, 'Flying', 'Dragon', 'Ground', 'Fairy', 'Grass',\n",
+       "       'Fighting', 'Psychic', 'Steel', 'Ice', 'Rock', 'Dark', 'Water',\n",
+       "       'Electric', 'Fire', 'Ghost', 'Bug', 'Normal'], dtype=object)"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df[\"Type 2\"].unique()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Name</th>\n",
+       "      <th>Type 1</th>\n",
+       "      <th>Type 2</th>\n",
+       "      <th>HP</th>\n",
+       "      <th>Attack</th>\n",
+       "      <th>Defense</th>\n",
+       "      <th>Sp. Atk</th>\n",
+       "      <th>Sp. Def</th>\n",
+       "      <th>Speed</th>\n",
+       "      <th>Generation</th>\n",
+       "      <th>Legendary</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>275</th>\n",
+       "      <td>Mega Sceptile</td>\n",
+       "      <td>Grass</td>\n",
+       "      <td>Dragon</td>\n",
+       "      <td>70</td>\n",
+       "      <td>110</td>\n",
+       "      <td>75</td>\n",
+       "      <td>145</td>\n",
+       "      <td>85</td>\n",
+       "      <td>145</td>\n",
+       "      <td>3</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "              Name Type 1  Type 2  HP  Attack  Defense  Sp. Atk  Sp. Def  \\\n",
+       "275  Mega Sceptile  Grass  Dragon  70     110       75      145       85   \n",
+       "\n",
+       "     Speed  Generation  Legendary  \n",
+       "275    145           3      False  "
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "both_types = df[(\n",
+    "        (df[\"Type 1\"] == \"Dragon\") |\n",
+    "        (df[\"Type 2\"] == \"Dragon\"))\n",
+    "    &\n",
+    "    ((df[\"Type 1\"] == \"Grass\") |\n",
+    "    (df[\"Type 2\"] == \"Grass\")\n",
+    ")]\n",
+    "\n",
+    "both_types"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Index([275], dtype='int64')"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "overlap_pokemon = both_types.index\n",
+    "overlap_pokemon"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "- We posit that Pokemons of type Dragon have, on average, more HP stats than Grass. Choose the propper test and, with 5% significance, comment your findings."
+    "- We posit that Pokemons of type Dragon have, on average, more HP stats than Grass. Choose the proper test and, with 5% significance, comment your findings."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [],
    "source": [
-    "#code here"
+    "# H0: dragon_mean_hp <= grass_mean_hp\n",
+    "# H1: dragon__mean_hp > grass_mean_hp\n",
+    "\n",
+    "alpha = 0.05 #significance level"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "7       78\n",
+      "159     41\n",
+      "160     61\n",
+      "161     91\n",
+      "196     90\n",
+      "249     75\n",
+      "360     50\n",
+      "361     80\n",
+      "365     75\n",
+      "366     75\n",
+      "406     45\n",
+      "407     65\n",
+      "408     95\n",
+      "409     95\n",
+      "417     80\n",
+      "418     80\n",
+      "419     80\n",
+      "420     80\n",
+      "425    105\n",
+      "426    105\n",
+      "491     58\n",
+      "492     68\n",
+      "493    108\n",
+      "494    108\n",
+      "540    100\n",
+      "541     90\n",
+      "544    150\n",
+      "545    150\n",
+      "671     46\n",
+      "672     66\n",
+      "673     76\n",
+      "682     77\n",
+      "694     52\n",
+      "695     72\n",
+      "696     92\n",
+      "706    100\n",
+      "707    100\n",
+      "710    125\n",
+      "711    125\n",
+      "712    125\n",
+      "761     65\n",
+      "766     58\n",
+      "767     82\n",
+      "774     45\n",
+      "775     68\n",
+      "776     90\n",
+      "790     40\n",
+      "791     85\n",
+      "794    108\n",
+      "Name: HP, dtype: int64\n",
+      "0      45\n",
+      "1      60\n",
+      "2      80\n",
+      "3      80\n",
+      "48     45\n",
+      "       ..\n",
+      "783    59\n",
+      "784    65\n",
+      "785    55\n",
+      "786    75\n",
+      "787    85\n",
+      "Name: HP, Length: 94, dtype: int64\n"
+     ]
+    }
+   ],
+   "source": [
+    "dragon_hp = df[((df[\"Type 1\"] == \"Dragon\") | (df[\"Type 2\"] == \"Dragon\")) & (~df.index.isin(overlap_pokemon))][\"HP\"]\n",
+    "grass_hp = df[((df[\"Type 1\"] == \"Grass\") | (df[\"Type 2\"] == \"Grass\")) & (~df.index.isin(overlap_pokemon))][\"HP\"]\n",
+    "print(dragon_hp)\n",
+    "print(grass_hp)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "np.float64(83.16326530612245)"
+      ]
+     },
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dragon_hp.mean()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "np.float64(66.01063829787235)"
+      ]
+     },
+     "execution_count": 32,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "grass_hp.mean()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "5.060530308690885e-05\n"
+     ]
+    }
+   ],
+   "source": [
+    "p_value = st.ttest_ind(dragon_hp, grass_hp, equal_var=False, alternative = \"greater\").pvalue\n",
+    "print(p_value)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H0 can be rejected\n"
+     ]
+    }
+   ],
+   "source": [
+    "#Decision-making\n",
+    "if p_value < alpha:\n",
+    "    print(\"H0 can be rejected\")\n",
+    "else:\n",
+    "    print(\"Fail to reject H0\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "- Since the H0 was rejected, pokemon of the dragon type have statistically significant higher average HP than grass types."
    ]
   },
   {
@@ -313,11 +632,77 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 44,
    "metadata": {},
    "outputs": [],
    "source": [
-    "#code here"
+    "# H0: lengendary_pokemons = non-legendary_pokemons\n",
+    "# H1: lengendary_pokemons != non-legendary_pokemons\n",
+    "alpha = 0.05"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "HP\n",
+      "P-value: 0.00000\n",
+      "Reject H0\n",
+      "\n",
+      "Attack\n",
+      "P-value: 0.00000\n",
+      "Reject H0\n",
+      "\n",
+      "Defense\n",
+      "P-value: 0.00000\n",
+      "Reject H0\n",
+      "\n",
+      "Sp. Atk\n",
+      "P-value: 0.00000\n",
+      "Reject H0\n",
+      "\n",
+      "Sp. Def\n",
+      "P-value: 0.00000\n",
+      "Reject H0\n",
+      "\n",
+      "Speed\n",
+      "P-value: 0.00000\n",
+      "Reject H0\n"
+     ]
+    }
+   ],
+   "source": [
+    "stats = [\"HP\", \"Attack\", \"Defense\", \"Sp. Atk\", \"Sp. Def\", \"Speed\"]\n",
+    "        \n",
+    "legendary = df[df[\"Legendary\"] == True]\n",
+    "non_legendary = df[df[\"Legendary\"] == False]\n",
+    "\n",
+    "for stat in stats:\n",
+    "    p_value = st.ttest_ind(\n",
+    "        legendary[stat],\n",
+    "        non_legendary[stat],\n",
+    "        equal_var=False).pvalue\n",
+    "\n",
+    "    print(f\"\\n{stat}\")\n",
+    "    print(f\"P-value: {p_value:.5f}\")\n",
+    "\n",
+    "    if p_value < alpha:\n",
+    "        print(\"Reject H0\")\n",
+    "    else:\n",
+    "        print(\"Fail to reject H0\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "- At the 5% significance level, the p-value for all statistics  is less than 0.05. Therefore, we reject the H0 for all six stats. So, there is sufficient statistical evidence that legendary and non-legendary pokemons differ significantly in each of the selected stats."
    ]
   },
   {
@@ -337,7 +722,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 48,
    "metadata": {},
    "outputs": [
     {
@@ -453,7 +838,7 @@
        "4       624.0       262.0         1.9250             65500.0  "
       ]
      },
-     "execution_count": 5,
+     "execution_count": 48,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -483,10 +868,260 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 50,
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "# H0: house_close <= house_far\n",
+    "# H1: house_close > house_far\n",
+    "\n",
+    "def euclidean_distance(x1, y1, x2, y2):\n",
+    "    return np.sqrt((x2 - x1)**2 + (y2 - y1)**2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df[\"distance_school\"] = euclidean_distance(\n",
+    "    df[\"longitude\"],\n",
+    "    df[\"latitude\"],\n",
+    "    -118,\n",
+    "    34\n",
+    ")\n",
+    "\n",
+    "df[\"distance_hospital\"] = euclidean_distance(\n",
+    "    df[\"longitude\"],\n",
+    "    df[\"latitude\"],\n",
+    "    -122,\n",
+    "    37\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>longitude</th>\n",
+       "      <th>latitude</th>\n",
+       "      <th>housing_median_age</th>\n",
+       "      <th>total_rooms</th>\n",
+       "      <th>total_bedrooms</th>\n",
+       "      <th>population</th>\n",
+       "      <th>households</th>\n",
+       "      <th>median_income</th>\n",
+       "      <th>median_house_value</th>\n",
+       "      <th>distance_school</th>\n",
+       "      <th>distance_hospital</th>\n",
+       "      <th>close</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>-114.31</td>\n",
+       "      <td>34.19</td>\n",
+       "      <td>15.0</td>\n",
+       "      <td>5612.0</td>\n",
+       "      <td>1283.0</td>\n",
+       "      <td>1015.0</td>\n",
+       "      <td>472.0</td>\n",
+       "      <td>1.4936</td>\n",
+       "      <td>66900.0</td>\n",
+       "      <td>3.694888</td>\n",
+       "      <td>8.187319</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>-114.47</td>\n",
+       "      <td>34.40</td>\n",
+       "      <td>19.0</td>\n",
+       "      <td>7650.0</td>\n",
+       "      <td>1901.0</td>\n",
+       "      <td>1129.0</td>\n",
+       "      <td>463.0</td>\n",
+       "      <td>1.8200</td>\n",
+       "      <td>80100.0</td>\n",
+       "      <td>3.552591</td>\n",
+       "      <td>7.966235</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>-114.56</td>\n",
+       "      <td>33.69</td>\n",
+       "      <td>17.0</td>\n",
+       "      <td>720.0</td>\n",
+       "      <td>174.0</td>\n",
+       "      <td>333.0</td>\n",
+       "      <td>117.0</td>\n",
+       "      <td>1.6509</td>\n",
+       "      <td>85700.0</td>\n",
+       "      <td>3.453940</td>\n",
+       "      <td>8.143077</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>-114.57</td>\n",
+       "      <td>33.64</td>\n",
+       "      <td>14.0</td>\n",
+       "      <td>1501.0</td>\n",
+       "      <td>337.0</td>\n",
+       "      <td>515.0</td>\n",
+       "      <td>226.0</td>\n",
+       "      <td>3.1917</td>\n",
+       "      <td>73400.0</td>\n",
+       "      <td>3.448840</td>\n",
+       "      <td>8.154416</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>-114.57</td>\n",
+       "      <td>33.57</td>\n",
+       "      <td>20.0</td>\n",
+       "      <td>1454.0</td>\n",
+       "      <td>326.0</td>\n",
+       "      <td>624.0</td>\n",
+       "      <td>262.0</td>\n",
+       "      <td>1.9250</td>\n",
+       "      <td>65500.0</td>\n",
+       "      <td>3.456848</td>\n",
+       "      <td>8.183508</td>\n",
+       "      <td>False</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   longitude  latitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
+       "0    -114.31     34.19                15.0       5612.0          1283.0   \n",
+       "1    -114.47     34.40                19.0       7650.0          1901.0   \n",
+       "2    -114.56     33.69                17.0        720.0           174.0   \n",
+       "3    -114.57     33.64                14.0       1501.0           337.0   \n",
+       "4    -114.57     33.57                20.0       1454.0           326.0   \n",
+       "\n",
+       "   population  households  median_income  median_house_value  distance_school  \\\n",
+       "0      1015.0       472.0         1.4936             66900.0         3.694888   \n",
+       "1      1129.0       463.0         1.8200             80100.0         3.552591   \n",
+       "2       333.0       117.0         1.6509             85700.0         3.453940   \n",
+       "3       515.0       226.0         3.1917             73400.0         3.448840   \n",
+       "4       624.0       262.0         1.9250             65500.0         3.456848   \n",
+       "\n",
+       "   distance_hospital  close  \n",
+       "0           8.187319  False  \n",
+       "1           7.966235  False  \n",
+       "2           8.143077  False  \n",
+       "3           8.154416  False  \n",
+       "4           8.183508  False  "
+      ]
+     },
+     "execution_count": 55,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df[\"close\"] = ((df[\"distance_school\"] < 0.5) | (df[\"distance_hospital\"] < 0.5))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 56,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "close_houses = df[df[\"close\"]][\"median_house_value\"]\n",
+    "far_houses = df[~df[\"close\"]][\"median_house_value\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1.5032478884296307e-301\n"
+     ]
+    }
+   ],
+   "source": [
+    "p_value = st.ttest_ind(\n",
+    "    close_houses,\n",
+    "    far_houses,\n",
+    "    equal_var=False,\n",
+    "    alternative=\"greater\").pvalue\n",
+    "\n",
+    "print(p_value)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Reject H0\n"
+     ]
+    }
+   ],
+   "source": [
+    "alpha = 0.05\n",
+    "\n",
+    "if p_value < alpha:\n",
+    "    print(\"Reject H0\")\n",
+    "else:\n",
+    "    print(\"Fail to reject H0\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "- There is sufficient statistical evidence to conclude that houses located within 0.50 units of either a school or a hospital have a higher mean house value than houses located farther away."
+   ]
   },
   {
    "cell_type": "code",
@@ -498,7 +1133,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -512,9 +1147,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.9"
+   "version": "3.13.5"
   }
  },
  "nbformat": 4,
- "nbformat_minor": 2
+ "nbformat_minor": 4
 }