diff --git a/lab-hypothesis-testing.ipynb b/lab-hypothesis-testing.ipynb
index 0cc26d5..d047a06 100644
--- a/lab-hypothesis-testing.ipynb
+++ b/lab-hypothesis-testing.ipynb
@@ -38,7 +38,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 165,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -51,7 +51,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 166,
    "metadata": {},
    "outputs": [
     {
@@ -278,7 +278,7 @@
        "[800 rows x 11 columns]"
       ]
      },
-     "execution_count": 3,
+     "execution_count": 166,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -288,56 +288,1433 @@
     "df"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 167,
+   "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>type1</th>\n",
+       "      <th>type2</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    type1   type2  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": 167,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df.columns=df.columns.str.strip().str.lower().str.replace('.', '_').str.replace(' ', '')\n",
+    "df"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 168,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df.isna().sum()\n",
+    "df=df.dropna().reset_index(drop=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 169,
+   "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>type1</th>\n",
+       "      <th>type2</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>Charizard</td>\n",
+       "      <td>Fire</td>\n",
+       "      <td>Flying</td>\n",
+       "      <td>78</td>\n",
+       "      <td>84</td>\n",
+       "      <td>78</td>\n",
+       "      <td>109</td>\n",
+       "      <td>85</td>\n",
+       "      <td>100</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>409</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>410</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>411</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>412</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>413</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>414 rows × 11 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "               name    type1   type2  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         Charizard     Fire  Flying  78      84       78     109      85   \n",
+       "..              ...      ...     ...  ..     ...      ...     ...     ...   \n",
+       "409         Diancie     Rock   Fairy  50     100      150     100     150   \n",
+       "410    Mega Diancie     Rock   Fairy  50     160      110     160     110   \n",
+       "411  Hoopa Confined  Psychic   Ghost  80     110       60     150     130   \n",
+       "412   Hoopa Unbound  Psychic    Dark  80     160       60     170     130   \n",
+       "413       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      100           1      False  \n",
+       "..     ...         ...        ...  \n",
+       "409     50           6       True  \n",
+       "410    110           6       True  \n",
+       "411     70           6       True  \n",
+       "412     80           6       True  \n",
+       "413     70           6       True  \n",
+       "\n",
+       "[414 rows x 11 columns]"
+      ]
+     },
+     "execution_count": 169,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df"
+   ]
+  },
+  {
+   "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."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# H0: Grp1_mean <= Grp2_mean\n",
+    "# H1: Grp1_mean > Grp2_mean"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 170,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0       45\n",
+       "1       60\n",
+       "2       80\n",
+       "3       80\n",
+       "24      45\n",
+       "25      60\n",
+       "26      75\n",
+       "32      50\n",
+       "33      65\n",
+       "34      80\n",
+       "55      60\n",
+       "56      95\n",
+       "94      35\n",
+       "95      55\n",
+       "96      75\n",
+       "133     70\n",
+       "145     70\n",
+       "146     90\n",
+       "157     60\n",
+       "172     50\n",
+       "181     70\n",
+       "196     99\n",
+       "215     95\n",
+       "223     40\n",
+       "224     60\n",
+       "256     60\n",
+       "257     90\n",
+       "258     90\n",
+       "281    100\n",
+       "300     40\n",
+       "301     60\n",
+       "321     69\n",
+       "322    114\n",
+       "327     44\n",
+       "328     74\n",
+       "349     91\n",
+       "364     88\n",
+       "Name: hp, dtype: int64"
+      ]
+     },
+     "execution_count": 170,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "grp_B=df[df[\"type1\"]==\"Grass\"][\"hp\"]\n",
+    "grp_B"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 171,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "76      91\n",
+       "183     75\n",
+       "184     75\n",
+       "201     95\n",
+       "202     95\n",
+       "207     80\n",
+       "208     80\n",
+       "209     80\n",
+       "210     80\n",
+       "212    105\n",
+       "213    105\n",
+       "245     58\n",
+       "246     68\n",
+       "247    108\n",
+       "248    108\n",
+       "352    100\n",
+       "353    100\n",
+       "356    125\n",
+       "357    125\n",
+       "358    125\n",
+       "408    108\n",
+       "Name: hp, dtype: int64"
+      ]
+     },
+     "execution_count": 171,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "grp_A=df[df[\"type1\"]==\"Dragon\"][\"hp\"]\n",
+    "grp_A"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 172,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "TtestResult(statistic=4.649881427485321, pvalue=2.068191387085888e-05, df=56.0)"
+      ]
+     },
+     "execution_count": 172,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from scipy import stats\n",
+    "# This returns the t-statistic and the p-value\n",
+    "stats.ttest_ind(grp_A, grp_B)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 173,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# H0: Grp1_mean <= Grp2_mean\n",
+    "# H1: Grp1_mean > Grp2_mean\n",
+    "## The p-value=2.06e-05 is lower than a significance level of 0.05, we fail to reject H0 and support that Grp 1 has more stats than to Grp2."
+   ]
+  },
+  {
+   "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": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# H0: Legendary Pokemons have same stats (HP, Attack, Defense, Sp.Atk, Sp.Def, Speed) as Non-legendary\n",
+    "# H1: Legendary Pokemons have different stats (HP, Attack, Defense, Sp.Atk, Sp.Def, Speed) compared to Non-legendary"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 174,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Separate the groups based on the 'legendary' column\n",
+    "stats=[\"hp\", \"attack\", \"defense\", \"sp_atk\", \"sp_def\", \"speed\",\"legendary\"]\n",
+    "df_stats = df[stats]\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 175,
+   "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>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>legendary</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\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>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\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>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\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>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\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>False</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>78</td>\n",
+       "      <td>84</td>\n",
+       "      <td>78</td>\n",
+       "      <td>109</td>\n",
+       "      <td>85</td>\n",
+       "      <td>100</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",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>409</th>\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>True</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>410</th>\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>True</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>411</th>\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>True</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>412</th>\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>True</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>413</th>\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>True</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>414 rows × 7 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "     hp  attack  defense  sp_atk  sp_def  speed  legendary\n",
+       "0    45      49       49      65      65     45      False\n",
+       "1    60      62       63      80      80     60      False\n",
+       "2    80      82       83     100     100     80      False\n",
+       "3    80     100      123     122     120     80      False\n",
+       "4    78      84       78     109      85    100      False\n",
+       "..   ..     ...      ...     ...     ...    ...        ...\n",
+       "409  50     100      150     100     150     50       True\n",
+       "410  50     160      110     160     110    110       True\n",
+       "411  80     110       60     150     130     70       True\n",
+       "412  80     160       60     170     130     80       True\n",
+       "413  80     110      120     130      90     70       True\n",
+       "\n",
+       "[414 rows x 7 columns]"
+      ]
+     },
+     "execution_count": 175,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df_stats"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 176,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from statsmodels.multivariate.manova import MANOVA"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 180,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "                   Multivariate linear model\n",
+      "================================================================\n",
+      "                                                                \n",
+      "----------------------------------------------------------------\n",
+      "       Intercept         Value  Num DF  Den DF   F Value  Pr > F\n",
+      "----------------------------------------------------------------\n",
+      "          Wilks' lambda  0.0530 6.0000 407.0000 1211.8954 0.0000\n",
+      "         Pillai's trace  0.9470 6.0000 407.0000 1211.8954 0.0000\n",
+      " Hotelling-Lawley trace 17.8658 6.0000 407.0000 1211.8954 0.0000\n",
+      "    Roy's greatest root 17.8658 6.0000 407.0000 1211.8954 0.0000\n",
+      "----------------------------------------------------------------\n",
+      "                                                                \n",
+      "----------------------------------------------------------------\n",
+      "          legendary        Value  Num DF  Den DF  F Value Pr > F\n",
+      "----------------------------------------------------------------\n",
+      "             Wilks' lambda 0.7117 6.0000 407.0000 27.4810 0.0000\n",
+      "            Pillai's trace 0.2883 6.0000 407.0000 27.4810 0.0000\n",
+      "    Hotelling-Lawley trace 0.4051 6.0000 407.0000 27.4810 0.0000\n",
+      "       Roy's greatest root 0.4051 6.0000 407.0000 27.4810 0.0000\n",
+      "================================================================\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "\n",
+    "# Define the formula: all six stats explained by the 'legendary' status\n",
+    "formula = 'hp + attack + defense + sp_atk + sp_def + speed ~ legendary'\n",
+    "\n",
+    "# Run the MANOVA model\n",
+    "manova = MANOVA.from_formula(formula, data=df_stats)\n",
+    "\n",
+    "# Get the multivariate test results (Focus on Wilks' lambda)\n",
+    "manova_results = manova.mv_test()\n",
+    "print(manova_results)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# The p_value of all four test is less than 0.05 so we reject the null hypothesis\n",
+    "# Obtained result supports the claim that Legendary Pokemons have different stats (HP, Attack, Defense, Sp.Atk, Sp.Def, Speed) compared to Non-legendary "
+   ]
+  },
+  {
+   "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": 181,
+   "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": 181,
+     "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 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 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": 182,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Requirement already satisfied: geopy in c:\\users\\hp\\anaconda3\\lib\\site-packages (2.4.1)\n",
+      "Requirement already satisfied: pandas in c:\\users\\hp\\anaconda3\\lib\\site-packages (2.3.3)\n",
+      "Requirement already satisfied: geographiclib<3,>=1.52 in c:\\users\\hp\\anaconda3\\lib\\site-packages (from geopy) (2.1)\n",
+      "Requirement already satisfied: numpy>=1.26.0 in c:\\users\\hp\\anaconda3\\lib\\site-packages (from pandas) (1.26.4)\n",
+      "Requirement already satisfied: python-dateutil>=2.8.2 in c:\\users\\hp\\anaconda3\\lib\\site-packages (from pandas) (2.9.0.post0)\n",
+      "Requirement already satisfied: pytz>=2020.1 in c:\\users\\hp\\anaconda3\\lib\\site-packages (from pandas) (2024.1)\n",
+      "Requirement already satisfied: tzdata>=2022.7 in c:\\users\\hp\\anaconda3\\lib\\site-packages (from pandas) (2023.3)\n",
+      "Requirement already satisfied: six>=1.5 in c:\\users\\hp\\anaconda3\\lib\\site-packages (from python-dateutil>=2.8.2->pandas) (1.16.0)\n",
+      "Note: you may need to restart the kernel to use updated packages.\n"
+     ]
+    }
+   ],
+   "source": [
+    "pip install geopy pandas"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 183,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# H0: Houses close to either a school or a hospital are more expensive.\n",
+    "# H1: houses far from either a school or a hospital are more expensive."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 184,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from geopy.distance import great_circle"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 185,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\n",
+    "def calculate_great_circle_distance(row,target_point):\n",
+    "    \n",
+    "    # Point 1 (Start) must be (latitude, longitude)\n",
+    "    start_point = (row['latitude'], row['longitude'])\n",
+    "    \n",
+    "    # Point 2 (End) must be (latitude, longitude)\n",
+    "    end_point = target_point\n",
+    "    \n",
+    "    # The great_circle function returns a distance object; we extract miles/km\n",
+    "        # Returning distance in Kilometers (you can use .miles, .meters, etc.)\n",
+    "    distance_km = great_circle(start_point, end_point).km\n",
+    "    return distance_km"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 186,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "school_point = (34.00, -118.00) \n",
+    "hospital_point = (37.00, -122.00) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 187,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df[\"distance_school\"]=df.apply(calculate_great_circle_distance,axis=1, target_point=school_point)\n",
+    "df[\"distance_hospital\"]=df.apply(calculate_great_circle_distance,axis=1, target_point=hospital_point)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 188,
+   "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",
+       "    </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>340.418792</td>\n",
+       "      <td>761.974459</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>327.659611</td>\n",
+       "      <td>738.576332</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>319.542519</td>\n",
+       "      <td>768.308921</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>319.365481</td>\n",
+       "      <td>770.371666</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>320.561844</td>\n",
+       "      <td>774.421877</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>16995</th>\n",
+       "      <td>-124.26</td>\n",
+       "      <td>40.58</td>\n",
+       "      <td>52.0</td>\n",
+       "      <td>2217.0</td>\n",
+       "      <td>394.0</td>\n",
+       "      <td>907.0</td>\n",
+       "      <td>369.0</td>\n",
+       "      <td>2.3571</td>\n",
+       "      <td>111400.0</td>\n",
+       "      <td>917.047590</td>\n",
+       "      <td>443.615947</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>16996</th>\n",
+       "      <td>-124.27</td>\n",
+       "      <td>40.69</td>\n",
+       "      <td>36.0</td>\n",
+       "      <td>2349.0</td>\n",
+       "      <td>528.0</td>\n",
+       "      <td>1194.0</td>\n",
+       "      <td>465.0</td>\n",
+       "      <td>2.5179</td>\n",
+       "      <td>79000.0</td>\n",
+       "      <td>927.102523</td>\n",
+       "      <td>454.929344</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>16997</th>\n",
+       "      <td>-124.30</td>\n",
+       "      <td>41.84</td>\n",
+       "      <td>17.0</td>\n",
+       "      <td>2677.0</td>\n",
+       "      <td>531.0</td>\n",
+       "      <td>1244.0</td>\n",
+       "      <td>456.0</td>\n",
+       "      <td>3.0313</td>\n",
+       "      <td>103600.0</td>\n",
+       "      <td>1031.462839</td>\n",
+       "      <td>573.239315</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>16998</th>\n",
+       "      <td>-124.30</td>\n",
+       "      <td>41.80</td>\n",
+       "      <td>19.0</td>\n",
+       "      <td>2672.0</td>\n",
+       "      <td>552.0</td>\n",
+       "      <td>1298.0</td>\n",
+       "      <td>478.0</td>\n",
+       "      <td>1.9797</td>\n",
+       "      <td>85800.0</td>\n",
+       "      <td>1027.794143</td>\n",
+       "      <td>569.086288</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>16999</th>\n",
+       "      <td>-124.35</td>\n",
+       "      <td>40.54</td>\n",
+       "      <td>52.0</td>\n",
+       "      <td>1820.0</td>\n",
+       "      <td>300.0</td>\n",
+       "      <td>806.0</td>\n",
+       "      <td>270.0</td>\n",
+       "      <td>3.0147</td>\n",
+       "      <td>94600.0</td>\n",
+       "      <td>918.431001</td>\n",
+       "      <td>443.183095</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>17000 rows × 11 columns</p>\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",
+       "16995    -124.26     40.58                52.0       2217.0           394.0   \n",
+       "16996    -124.27     40.69                36.0       2349.0           528.0   \n",
+       "16997    -124.30     41.84                17.0       2677.0           531.0   \n",
+       "16998    -124.30     41.80                19.0       2672.0           552.0   \n",
+       "16999    -124.35     40.54                52.0       1820.0           300.0   \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   \n",
+       "...           ...         ...            ...                 ...   \n",
+       "16995       907.0       369.0         2.3571            111400.0   \n",
+       "16996      1194.0       465.0         2.5179             79000.0   \n",
+       "16997      1244.0       456.0         3.0313            103600.0   \n",
+       "16998      1298.0       478.0         1.9797             85800.0   \n",
+       "16999       806.0       270.0         3.0147             94600.0   \n",
+       "\n",
+       "       distance_school  distance_hospital  \n",
+       "0           340.418792         761.974459  \n",
+       "1           327.659611         738.576332  \n",
+       "2           319.542519         768.308921  \n",
+       "3           319.365481         770.371666  \n",
+       "4           320.561844         774.421877  \n",
+       "...                ...                ...  \n",
+       "16995       917.047590         443.615947  \n",
+       "16996       927.102523         454.929344  \n",
+       "16997      1031.462839         573.239315  \n",
+       "16998      1027.794143         569.086288  \n",
+       "16999       918.431001         443.183095  \n",
+       "\n",
+       "[17000 rows x 11 columns]"
+      ]
+     },
+     "execution_count": 188,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 189,
    "metadata": {},
    "outputs": [],
    "source": [
-    "#code here"
-   ]
-  },
-  {
-   "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"
+    "cond1=df[\"distance_school\"]<0.5\n",
+    "cond2=df[\"distance_hospital\"]<0.5"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 190,
    "metadata": {},
    "outputs": [],
    "source": [
-    "#code here"
-   ]
-  },
-  {
-   "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"
+    "df[\"distance_category\"] = np.where(\n",
+    "    cond1 | cond2,\"close\", \"far\" )"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 191,
    "metadata": {},
    "outputs": [
     {
@@ -370,6 +1747,9 @@
        "      <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>distance_category</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
@@ -384,6 +1764,9 @@
        "      <td>472.0</td>\n",
        "      <td>1.4936</td>\n",
        "      <td>66900.0</td>\n",
+       "      <td>340.418792</td>\n",
+       "      <td>761.974459</td>\n",
+       "      <td>far</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
@@ -396,6 +1779,9 @@
        "      <td>463.0</td>\n",
        "      <td>1.8200</td>\n",
        "      <td>80100.0</td>\n",
+       "      <td>327.659611</td>\n",
+       "      <td>738.576332</td>\n",
+       "      <td>far</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
@@ -408,6 +1794,9 @@
        "      <td>117.0</td>\n",
        "      <td>1.6509</td>\n",
        "      <td>85700.0</td>\n",
+       "      <td>319.542519</td>\n",
+       "      <td>768.308921</td>\n",
+       "      <td>far</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
@@ -420,6 +1809,9 @@
        "      <td>226.0</td>\n",
        "      <td>3.1917</td>\n",
        "      <td>73400.0</td>\n",
+       "      <td>319.365481</td>\n",
+       "      <td>770.371666</td>\n",
+       "      <td>far</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
@@ -432,53 +1824,237 @@
        "      <td>262.0</td>\n",
        "      <td>1.9250</td>\n",
        "      <td>65500.0</td>\n",
+       "      <td>320.561844</td>\n",
+       "      <td>774.421877</td>\n",
+       "      <td>far</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",
+       "      <td>...</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>16995</th>\n",
+       "      <td>-124.26</td>\n",
+       "      <td>40.58</td>\n",
+       "      <td>52.0</td>\n",
+       "      <td>2217.0</td>\n",
+       "      <td>394.0</td>\n",
+       "      <td>907.0</td>\n",
+       "      <td>369.0</td>\n",
+       "      <td>2.3571</td>\n",
+       "      <td>111400.0</td>\n",
+       "      <td>917.047590</td>\n",
+       "      <td>443.615947</td>\n",
+       "      <td>far</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>16996</th>\n",
+       "      <td>-124.27</td>\n",
+       "      <td>40.69</td>\n",
+       "      <td>36.0</td>\n",
+       "      <td>2349.0</td>\n",
+       "      <td>528.0</td>\n",
+       "      <td>1194.0</td>\n",
+       "      <td>465.0</td>\n",
+       "      <td>2.5179</td>\n",
+       "      <td>79000.0</td>\n",
+       "      <td>927.102523</td>\n",
+       "      <td>454.929344</td>\n",
+       "      <td>far</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>16997</th>\n",
+       "      <td>-124.30</td>\n",
+       "      <td>41.84</td>\n",
+       "      <td>17.0</td>\n",
+       "      <td>2677.0</td>\n",
+       "      <td>531.0</td>\n",
+       "      <td>1244.0</td>\n",
+       "      <td>456.0</td>\n",
+       "      <td>3.0313</td>\n",
+       "      <td>103600.0</td>\n",
+       "      <td>1031.462839</td>\n",
+       "      <td>573.239315</td>\n",
+       "      <td>far</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>16998</th>\n",
+       "      <td>-124.30</td>\n",
+       "      <td>41.80</td>\n",
+       "      <td>19.0</td>\n",
+       "      <td>2672.0</td>\n",
+       "      <td>552.0</td>\n",
+       "      <td>1298.0</td>\n",
+       "      <td>478.0</td>\n",
+       "      <td>1.9797</td>\n",
+       "      <td>85800.0</td>\n",
+       "      <td>1027.794143</td>\n",
+       "      <td>569.086288</td>\n",
+       "      <td>far</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>16999</th>\n",
+       "      <td>-124.35</td>\n",
+       "      <td>40.54</td>\n",
+       "      <td>52.0</td>\n",
+       "      <td>1820.0</td>\n",
+       "      <td>300.0</td>\n",
+       "      <td>806.0</td>\n",
+       "      <td>270.0</td>\n",
+       "      <td>3.0147</td>\n",
+       "      <td>94600.0</td>\n",
+       "      <td>918.431001</td>\n",
+       "      <td>443.183095</td>\n",
+       "      <td>far</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
+       "<p>17000 rows × 12 columns</p>\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",
+       "       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",
+       "16995    -124.26     40.58                52.0       2217.0           394.0   \n",
+       "16996    -124.27     40.69                36.0       2349.0           528.0   \n",
+       "16997    -124.30     41.84                17.0       2677.0           531.0   \n",
+       "16998    -124.30     41.80                19.0       2672.0           552.0   \n",
+       "16999    -124.35     40.54                52.0       1820.0           300.0   \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  "
+       "       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   \n",
+       "...           ...         ...            ...                 ...   \n",
+       "16995       907.0       369.0         2.3571            111400.0   \n",
+       "16996      1194.0       465.0         2.5179             79000.0   \n",
+       "16997      1244.0       456.0         3.0313            103600.0   \n",
+       "16998      1298.0       478.0         1.9797             85800.0   \n",
+       "16999       806.0       270.0         3.0147             94600.0   \n",
+       "\n",
+       "       distance_school  distance_hospital distance_category  \n",
+       "0           340.418792         761.974459               far  \n",
+       "1           327.659611         738.576332               far  \n",
+       "2           319.542519         768.308921               far  \n",
+       "3           319.365481         770.371666               far  \n",
+       "4           320.561844         774.421877               far  \n",
+       "...                ...                ...               ...  \n",
+       "16995       917.047590         443.615947               far  \n",
+       "16996       927.102523         454.929344               far  \n",
+       "16997      1031.462839         573.239315               far  \n",
+       "16998      1027.794143         569.086288               far  \n",
+       "16999       918.431001         443.183095               far  \n",
+       "\n",
+       "[17000 rows x 12 columns]"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 191,
      "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()"
+    "df"
    ]
   },
   {
-   "cell_type": "markdown",
+   "cell_type": "code",
+   "execution_count": 192,
    "metadata": {},
+   "outputs": [],
    "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",
-    " "
+    "# H0: avg_price_closer <= avg_price_far.\n",
+    "# H1: avg_price_closer > avg_price_far."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 193,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "## If the average price of houses closer to schools and hospitals is higher than houses far from these places then we support that they are expensive."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 194,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df_close=df[df[\"distance_category\"]==\"close\"][\"median_house_value\"]\n",
+    "df_far=df[df[\"distance_category\"]==\"far\"][\"median_house_value\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 195,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "13747    137500.0\n",
+       "Name: median_house_value, dtype: float64"
+      ]
+     },
+     "execution_count": 195,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df_close"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 196,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "TtestResult(statistic=-0.6018226451778325, pvalue=0.7263498868187508, df=16998.0)"
+      ]
+     },
+     "execution_count": 196,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from scipy import stats\n",
+    "# This returns the t-statistic and the p-value\n",
+    "stats.ttest_ind(df_close, df_far,alternative=\"greater\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 197,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "## The P-value is higher than 0.05 so we do not reject HO and support claim that average price for houses closer to school and houses --\n",
+    "## -- are not more expensive."
    ]
   },
   {
@@ -488,6 +2064,13 @@
    "outputs": [],
    "source": []
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -498,7 +2081,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -512,9 +2095,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.9"
+   "version": "3.12.7"
   }
  },
  "nbformat": 4,
- "nbformat_minor": 2
+ "nbformat_minor": 4
 }