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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Before your start:\n",
+    "- Read the README.md file\n",
+    "- Comment as much as you can and use the resources (README.md file)\n",
+    "- Happy learning!\n",
+    "\n",
+    "- **Consider a significance level of 5% for all tests.**"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# import numpy and pandas\n",
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "from scipy.stats import chi2_contingency\n",
+    "import scipy.stats as sts # stats\n",
+    "import statsmodels.api as sm\n",
+    "import statsmodels.formula.api as smf"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Challenge 1 - Independent Sample T-tests\n",
+    "\n",
+    "In this challenge, we will be using the Pokemon dataset. Before applying statistical methods to this data, let's first examine the data.\n",
+    "\n",
+    "To load the data, run the code below."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Run this code:\n",
+    "\n",
+    "pokemon = pd.read_csv('../pokemon.csv')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let's start off by looking at the `head` function in the cell below."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "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>#</th>\n",
+       "      <th>Name</th>\n",
+       "      <th>Type 1</th>\n",
+       "      <th>Type 2</th>\n",
+       "      <th>Total</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>1</td>\n",
+       "      <td>Bulbasaur</td>\n",
+       "      <td>Grass</td>\n",
+       "      <td>Poison</td>\n",
+       "      <td>318</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>2</td>\n",
+       "      <td>Ivysaur</td>\n",
+       "      <td>Grass</td>\n",
+       "      <td>Poison</td>\n",
+       "      <td>405</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>3</td>\n",
+       "      <td>Venusaur</td>\n",
+       "      <td>Grass</td>\n",
+       "      <td>Poison</td>\n",
+       "      <td>525</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>3</td>\n",
+       "      <td>VenusaurMega Venusaur</td>\n",
+       "      <td>Grass</td>\n",
+       "      <td>Poison</td>\n",
+       "      <td>625</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>4</td>\n",
+       "      <td>Charmander</td>\n",
+       "      <td>Fire</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>309</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",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   #                   Name Type 1  Type 2  Total  HP  Attack  Defense  \\\n",
+       "0  1              Bulbasaur  Grass  Poison    318  45      49       49   \n",
+       "1  2                Ivysaur  Grass  Poison    405  60      62       63   \n",
+       "2  3               Venusaur  Grass  Poison    525  80      82       83   \n",
+       "3  3  VenusaurMega Venusaur  Grass  Poison    625  80     100      123   \n",
+       "4  4             Charmander   Fire     NaN    309  39      52       43   \n",
+       "\n",
+       "   Sp. Atk  Sp. Def  Speed  Generation  Legendary  \n",
+       "0       65       65     45           1      False  \n",
+       "1       80       80     60           1      False  \n",
+       "2      100      100     80           1      False  \n",
+       "3      122      120     80           1      False  \n",
+       "4       60       50     65           1      False  "
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pokemon.head()\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The first thing we would like to do is compare the legendary Pokemon to the regular Pokemon. To do this, we should examine the data further. What is the count of legendary vs. non legendary Pokemons?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Legendary\n",
+       "False    735\n",
+       "True      65\n",
+       "Name: count, dtype: int64"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "type_pok=pokemon[\"Legendary\"].value_counts()\n",
+    "type_pok"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Compute the mean and standard deviation of the total points for both legendary and non-legendary Pokemon."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "637.3846153846154"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pokemon[pokemon[\"Legendary\"]==True][\"Total\"].mean()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "60.93738905315346"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pokemon[pokemon[\"Legendary\"]==True][\"Total\"].std()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "417.21360544217686"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pokemon[pokemon[\"Legendary\"]==False][\"Total\"].mean()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "106.76041745713022"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pokemon[pokemon[\"Legendary\"]==False][\"Total\"].std()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The computation of the mean might give us a clue regarding how the statistical test may turn out; However, it certainly does not prove whether there is a significant difference between the two groups.\n",
+    "\n",
+    "In the cell below, use the `ttest_ind` function in `scipy.stats` to compare the the total points for legendary and non-legendary Pokemon. Since we do not have any information about the population, assume the variances are not equal."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Your code here:\n",
+    "lendary=pokemon[pokemon[\"Legendary\"]==True][\"Total\"]\n",
+    "non_legendary=pokemon[pokemon[\"Legendary\"]==False][\"Total\"]\n",
+    "alpha=.05"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "t_stat, p_value = sts.ttest_ind(lendary, non_legendary, equal_var=False)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "25.8335743895517"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "t_stat"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "9.357954335957446e-47"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "p_value"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Reject the Null Hypothesis: There is sufficient evidence to conclude that the mean of points are different for legendary and non.\n"
+     ]
+    }
+   ],
+   "source": [
+    "if p_value<alpha:\n",
+    "    print(\"Reject the Null Hypothesis: There is sufficient evidence to conclude that the mean of points are different for legendary and non.\")\n",
+    "else:\n",
+    "    print(\"Fail to Reject the Null Hypothesis: The mean points for legendary and non  are not significantly different.\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "What do you conclude from this test? Write your conclusions below."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#The values tell me that there is a significant difference between legendary and non legendary pokemons\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "How about we try to compare the different types of pokemon? In the cell below, list the types of Pokemon from column `Type 1` and the count of each type."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "scrolled": true
+   },
+   "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>Type 1</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>Grass</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>Grass</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>Grass</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>Grass</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>Fire</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>...</th>\n",
+       "      <td>...</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>795</th>\n",
+       "      <td>Rock</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>796</th>\n",
+       "      <td>Rock</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>797</th>\n",
+       "      <td>Psychic</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>798</th>\n",
+       "      <td>Psychic</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>799</th>\n",
+       "      <td>Fire</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>800 rows × 1 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "      Type 1\n",
+       "0      Grass\n",
+       "1      Grass\n",
+       "2      Grass\n",
+       "3      Grass\n",
+       "4       Fire\n",
+       "..       ...\n",
+       "795     Rock\n",
+       "796     Rock\n",
+       "797  Psychic\n",
+       "798  Psychic\n",
+       "799     Fire\n",
+       "\n",
+       "[800 rows x 1 columns]"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pokemon_type1=pd.DataFrame(pokemon[\"Type 1\"])\n",
+    "pokemon_type1"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Since water is the largest group of Pokemon, compare the mean and standard deviation of water Pokemon to all other Pokemon."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 98,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "water=pokemon[pokemon[\"Type 1\"]==\"Water\"][\"Total\"]\n",
+    "other=pokemon[pokemon[\"Type 1\"]!=\"Water\"][\"Total\"]\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 100,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "430.45535714285717"
+      ]
+     },
+     "execution_count": 100,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "water.mean()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 102,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "435.85901162790697"
+      ]
+     },
+     "execution_count": 102,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "other.mean()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 104,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "113.18826606431458"
+      ]
+     },
+     "execution_count": 104,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "water.std()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 106,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "121.09168230208066"
+      ]
+     },
+     "execution_count": 106,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "other.std()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Perform a hypothesis test comparing the mean of total points for water Pokemon to all non-water Pokemon. Assume the variances are equal. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 108,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# alternative there is a change between all types and water\n",
+    "t_stat,p_value=sts.ttest_ind(water,other, equal_var=True)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 110,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "-0.4418547448849676"
+      ]
+     },
+     "execution_count": 110,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "t_stat"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 112,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.6587140317488793"
+      ]
+     },
+     "execution_count": 112,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "p_value"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Write your conclusion below."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'\\nthe pvalue is less than 0.05 which means that there is a significant difference between water and others.\\nWhich means that we can reject the null hypothesis.\\nAlso the t_Stat is says that water tends to have a bigger value, this because is positive.\\n'"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "\"\"\"\n",
+    "the pvalue is over than 0.05 which means that there is not a significant difference between water and others.\n",
+    "Which means that we can reject the alternative hypothesis.\n",
+    "\"\"\"\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Challenge 2 - Matched Pairs Test\n",
+    "\n",
+    "In this challenge we will compare dependent samples of data describing our Pokemon. Our goal is to see whether there is a significant difference between each Pokemon's defense and attack scores. Our hypothesis is that the defense and attack scores are equal. In the cell below, import the `ttest_rel` function from `scipy.stats` and compare the two columns to see if there is a statistically significant difference between them."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "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>#</th>\n",
+       "      <th>Name</th>\n",
+       "      <th>Type 1</th>\n",
+       "      <th>Type 2</th>\n",
+       "      <th>Total</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>1</td>\n",
+       "      <td>Bulbasaur</td>\n",
+       "      <td>Grass</td>\n",
+       "      <td>Poison</td>\n",
+       "      <td>318</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>2</td>\n",
+       "      <td>Ivysaur</td>\n",
+       "      <td>Grass</td>\n",
+       "      <td>Poison</td>\n",
+       "      <td>405</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",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   #       Name Type 1  Type 2  Total  HP  Attack  Defense  Sp. Atk  Sp. Def  \\\n",
+       "0  1  Bulbasaur  Grass  Poison    318  45      49       49       65       65   \n",
+       "1  2    Ivysaur  Grass  Poison    405  60      62       63       80       80   \n",
+       "\n",
+       "   Speed  Generation  Legendary  \n",
+       "0     45           1      False  \n",
+       "1     60           1      False  "
+      ]
+     },
+     "execution_count": 39,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pokemon.head(2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 114,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "defense=pokemon[\"Defense\"]\n",
+    "attack=pokemon[\"Attack\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 116,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "t_test,p_value=sts.ttest_rel(defense,attack)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 118,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "-4.325566393330478"
+      ]
+     },
+     "execution_count": 118,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "t_test"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 120,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1.7140303479358558e-05"
+      ]
+     },
+     "execution_count": 120,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "p_value"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Describe the results of the test in the cell below."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 123,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'\\nthis means that the hypothesis is right and the defense and attack scores are not equal with an inclination \\nto the attack to be higher\\n'"
+      ]
+     },
+     "execution_count": 123,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "\"\"\"\n",
+    "this means that the hypothesis is right and the defense and attack scores are not equal with an inclination \n",
+    "to the attack to be higher\n",
+    "\"\"\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We are also curious about whether therer is a significant difference between the mean of special defense and the mean of special attack. Perform the hypothesis test in the cell below. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 125,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "special_defense=pokemon[\"Sp. Def\"]\n",
+    "special_attack=pokemon[\"Sp. Atk\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 127,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "t_test,p_value=sts.ttest_rel(special_defense,special_attack)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 129,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "-0.853986188453353"
+      ]
+     },
+     "execution_count": 129,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "t_test\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 131,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.3933685997548122"
+      ]
+     },
+     "execution_count": 131,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "p_value"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Describe the results of the test in the cell below."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Because of the p_value is higher than 0.05 this means that the null hypothesis is correct and that there is \n",
+    "#no significant difference between special attack and special defense\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As you may recall, a two sample matched pairs test can also be expressed as a one sample test of the difference between the two dependent columns.\n",
+    "\n",
+    "Import the `ttest_1samp` function and perform a one sample t-test of the difference between defense and attack. Test the hypothesis that the difference between the means is zero. Confirm that the results of the test are the same."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 133,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "difference=pokemon[\"Defense\"]-pokemon[\"Attack\"]    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 153,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "t_stat,p_value=sts.ttest_1samp(difference,0,alternative=\"two-sided\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 155,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "-4.325566393330478"
+      ]
+     },
+     "execution_count": 155,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "t_stat"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 157,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1.7140303479358558e-05"
+      ]
+     },
+     "execution_count": 157,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "p_value"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\"\"\"\n",
+    "here we confirm that the null hypothesis that the difference between both is 0 is rejected\n",
+    "because the p value means that there is a significant difference between attack and defense\n",
+    "\"\"\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Bonus Challenge - The Chi-Square Test\n",
+    "\n",
+    "The Chi-Square test is used to determine whether there is a statistically significant difference in frequencies. In other words, we are testing whether there is a relationship between categorical variables or rather when the variables are independent. This test is an alternative to Fisher's exact test and is used in scenarios where sample sizes are larger. However, with a large enough sample size, both tests produce similar results. Read more about the Chi Squared test [here](https://en.wikipedia.org/wiki/Chi-squared_test).\n",
+    "\n",
+    "In the cell below, create a contingency table using `pd.crosstab` comparing whether a Pokemon is legenadary or not and whether the Type 1 of a Pokemon is water or not."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 141,
+   "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>Type 1</th>\n",
+       "      <th>Bug</th>\n",
+       "      <th>Dark</th>\n",
+       "      <th>Dragon</th>\n",
+       "      <th>Electric</th>\n",
+       "      <th>Fairy</th>\n",
+       "      <th>Fighting</th>\n",
+       "      <th>Fire</th>\n",
+       "      <th>Flying</th>\n",
+       "      <th>Ghost</th>\n",
+       "      <th>Grass</th>\n",
+       "      <th>Ground</th>\n",
+       "      <th>Ice</th>\n",
+       "      <th>Normal</th>\n",
+       "      <th>Poison</th>\n",
+       "      <th>Psychic</th>\n",
+       "      <th>Rock</th>\n",
+       "      <th>Steel</th>\n",
+       "      <th>Water</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>Legendary</th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>False</th>\n",
+       "      <td>69</td>\n",
+       "      <td>29</td>\n",
+       "      <td>20</td>\n",
+       "      <td>40</td>\n",
+       "      <td>16</td>\n",
+       "      <td>27</td>\n",
+       "      <td>47</td>\n",
+       "      <td>2</td>\n",
+       "      <td>30</td>\n",
+       "      <td>67</td>\n",
+       "      <td>28</td>\n",
+       "      <td>22</td>\n",
+       "      <td>96</td>\n",
+       "      <td>28</td>\n",
+       "      <td>43</td>\n",
+       "      <td>40</td>\n",
+       "      <td>23</td>\n",
+       "      <td>108</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>True</th>\n",
+       "      <td>0</td>\n",
+       "      <td>2</td>\n",
+       "      <td>12</td>\n",
+       "      <td>4</td>\n",
+       "      <td>1</td>\n",
+       "      <td>0</td>\n",
+       "      <td>5</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>3</td>\n",
+       "      <td>4</td>\n",
+       "      <td>2</td>\n",
+       "      <td>2</td>\n",
+       "      <td>0</td>\n",
+       "      <td>14</td>\n",
+       "      <td>4</td>\n",
+       "      <td>4</td>\n",
+       "      <td>4</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "Type 1     Bug  Dark  Dragon  Electric  Fairy  Fighting  Fire  Flying  Ghost  \\\n",
+       "Legendary                                                                      \n",
+       "False       69    29      20        40     16        27    47       2     30   \n",
+       "True         0     2      12         4      1         0     5       2      2   \n",
+       "\n",
+       "Type 1     Grass  Ground  Ice  Normal  Poison  Psychic  Rock  Steel  Water  \n",
+       "Legendary                                                                   \n",
+       "False         67      28   22      96      28       43    40     23    108  \n",
+       "True           3       4    2       2       0       14     4      4      4  "
+      ]
+     },
+     "execution_count": 141,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "cross=pd.crosstab(pokemon[\"Legendary\"],pokemon[\"Type 1\"])\n",
+    "cross"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Perform a chi-squared test using the `chi2_contingency` function in `scipy.stats`. You can read the documentation of the function [here](https://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.stats.chi2_contingency.html)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 143,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "5.118547414721704e-12"
+      ]
+     },
+     "execution_count": 143,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "_, chi2_pvalue, _, _  = chi2_contingency(cross)\n",
+    "\n",
+    "chi2_pvalue"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Based on a 95% confidence, should we reject the null hypothesis?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Yes vecause the pvalue is less than 0.05 which means we have enough information to reject null hypothesis\n",
+    "\n"
+   ]
+  },
+  {
+   "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": "3.12.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/your-code/main.ipynb b/your-code/main.ipynb
deleted file mode 100644
index cdc1acb..0000000
--- a/your-code/main.ipynb
+++ /dev/null
@@ -1,376 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Before your start:\n",
-    "- Read the README.md file\n",
-    "- Comment as much as you can and use the resources (README.md file)\n",
-    "- Happy learning!\n",
-    "\n",
-    "- **Consider a significance level of 5% for all tests.**"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# import numpy and pandas\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Challenge 1 - Independent Sample T-tests\n",
-    "\n",
-    "In this challenge, we will be using the Pokemon dataset. Before applying statistical methods to this data, let's first examine the data.\n",
-    "\n",
-    "To load the data, run the code below."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Run this code:\n",
-    "\n",
-    "pokemon = pd.read_csv('../pokemon.csv')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let's start off by looking at the `head` function in the cell below."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your code here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The first thing we would like to do is compare the legendary Pokemon to the regular Pokemon. To do this, we should examine the data further. What is the count of legendary vs. non legendary Pokemons?"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your code here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Compute the mean and standard deviation of the total points for both legendary and non-legendary Pokemon."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your code here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The computation of the mean might give us a clue regarding how the statistical test may turn out; However, it certainly does not prove whether there is a significant difference between the two groups.\n",
-    "\n",
-    "In the cell below, use the `ttest_ind` function in `scipy.stats` to compare the the total points for legendary and non-legendary Pokemon. Since we do not have any information about the population, assume the variances are not equal."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your code here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "What do you conclude from this test? Write your conclusions below."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your conclusions here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "How about we try to compare the different types of pokemon? In the cell below, list the types of Pokemon from column `Type 1` and the count of each type."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your code here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Since water is the largest group of Pokemon, compare the mean and standard deviation of water Pokemon to all other Pokemon."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your code here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Perform a hypothesis test comparing the mean of total points for water Pokemon to all non-water Pokemon. Assume the variances are equal. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your code here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Write your conclusion below."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your conclusions here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Challenge 2 - Matched Pairs Test\n",
-    "\n",
-    "In this challenge we will compare dependent samples of data describing our Pokemon. Our goal is to see whether there is a significant difference between each Pokemon's defense and attack scores. Our hypothesis is that the defense and attack scores are equal. In the cell below, import the `ttest_rel` function from `scipy.stats` and compare the two columns to see if there is a statistically significant difference between them."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your code here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Describe the results of the test in the cell below."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your conclusions here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We are also curious about whether therer is a significant difference between the mean of special defense and the mean of special attack. Perform the hypothesis test in the cell below. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your code here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Describe the results of the test in the cell below."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your conclusions here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "As you may recall, a two sample matched pairs test can also be expressed as a one sample test of the difference between the two dependent columns.\n",
-    "\n",
-    "Import the `ttest_1samp` function and perform a one sample t-test of the difference between defense and attack. Test the hypothesis that the difference between the means is zero. Confirm that the results of the test are the same."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your code here:\n",
-    "    \n",
-    "    "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Bonus Challenge - The Chi-Square Test\n",
-    "\n",
-    "The Chi-Square test is used to determine whether there is a statistically significant difference in frequencies. In other words, we are testing whether there is a relationship between categorical variables or rather when the variables are independent. This test is an alternative to Fisher's exact test and is used in scenarios where sample sizes are larger. However, with a large enough sample size, both tests produce similar results. Read more about the Chi Squared test [here](https://en.wikipedia.org/wiki/Chi-squared_test).\n",
-    "\n",
-    "In the cell below, create a contingency table using `pd.crosstab` comparing whether a Pokemon is legenadary or not and whether the Type 1 of a Pokemon is water or not."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your code here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Perform a chi-squared test using the `chi2_contingency` function in `scipy.stats`. You can read the documentation of the function [here](https://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.stats.chi2_contingency.html)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your code here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Based on a 95% confidence, should we reject the null hypothesis?"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Your answer here:\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
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-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.6.9"
-  }
- },
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