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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "ee314908",
+   "metadata": {},
+   "source": [
+    "# Lab | Inferential statistics - T-test & P-value"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "cafe0ae7-2c1f-4bfb-b8ce-91ec5f88a309",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "import math\n",
+    "import statistics\n",
+    "from scipy.stats import ttest_ind, norm"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "515aa25e",
+   "metadata": {},
+   "source": [
+    "## 1.  We will have another simple example on two sample t test (pooled- when the variances are equal). But this time this is a one sided t-test\n",
+    "\n",
+    "In a packing plant, a machine packs cartons with jars. It is supposed that a new machine will pack faster on the average than the machine currently used. To test that hypothesis, the times it takes each machine to pack ten cartons are recorded. The results, in seconds, are shown in the tables in the file `files_for_lab/machine.txt`.\n",
+    "Assume that there is sufficient evidence to conduct the t test, does the data provide sufficient evidence to show if one machine is better than the other\n",
+    "\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "024e25df-ad3f-41b9-9db0-d90a8cc6b12d",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "   new_machine  old_machine\n",
+      "0         42.1         42.7\n",
+      "1         41.0         43.6\n",
+      "2         41.3         43.8\n",
+      "3         41.8         43.3\n",
+      "4         42.4         42.5\n",
+      "5         42.8         43.5\n",
+      "6         43.2         43.1\n",
+      "7         42.3         41.7\n",
+      "8         41.8         44.0\n",
+      "9         42.7         44.1\n"
+     ]
+    }
+   ],
+   "source": [
+    "df = pd.read_excel('/Users/spicasumampouw/IronSpica/lab/Unit_7/lab-t-tests-p-values/files_for_lab/machine.xlsx')\n",
+    "print(df)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "c3dfe8ce-f6c7-4573-a71d-d2a88bd93068",
+   "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>count</th>\n",
+       "      <th>mean</th>\n",
+       "      <th>std</th>\n",
+       "      <th>min</th>\n",
+       "      <th>25%</th>\n",
+       "      <th>50%</th>\n",
+       "      <th>75%</th>\n",
+       "      <th>max</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>new_machine</th>\n",
+       "      <td>10.0</td>\n",
+       "      <td>42.14</td>\n",
+       "      <td>0.683455</td>\n",
+       "      <td>41.0</td>\n",
+       "      <td>41.8</td>\n",
+       "      <td>42.2</td>\n",
+       "      <td>42.625</td>\n",
+       "      <td>43.2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>old_machine</th>\n",
+       "      <td>10.0</td>\n",
+       "      <td>43.23</td>\n",
+       "      <td>0.749889</td>\n",
+       "      <td>41.7</td>\n",
+       "      <td>42.8</td>\n",
+       "      <td>43.4</td>\n",
+       "      <td>43.750</td>\n",
+       "      <td>44.1</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "             count   mean       std   min   25%   50%     75%   max\n",
+       "new_machine   10.0  42.14  0.683455  41.0  41.8  42.2  42.625  43.2\n",
+       "old_machine   10.0  43.23  0.749889  41.7  42.8  43.4  43.750  44.1"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df.describe().T"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 61,
+   "id": "f6a79e0b-0993-414a-aa32-1a1f4ea38b98",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sample_mean1 = df[\"new_machine\"].mean()\n",
+    "sample_mean2 = df[\"old_machine\"].mean()\n",
+    "sample_std1 = df[\"new_machine\"].std()\n",
+    "sample_std2 = df[\"old_machine\"].std()\n",
+    "n1 = len(df[\"new_machine\"])\n",
+    "n2 = len(df[\"old_machine\"])\n",
+    "\n",
+    "pop_mean = df[\"new_machine\"].mean()+df[\"old_machine\"].mean()\n",
+    "pop_std = df[\"new_machine\"].std()+df[\"old_machine\"].std()\n",
+    "n = len(df[\"new_machine\"])+len(df[\"old_machine\"])\n",
+    "\n",
+    "statistic1 = (sample_mean1 - pop_mean)/(pop_std/math.sqrt(n))\n",
+    "statistic2 = (sample_mean2 - pop_mean)/(pop_std/math.sqrt(n))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 62,
+   "id": "2ce0f7f1-7792-4e04-ad59-3360fcf187df",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Statistic1 is:  -134.8806821799226\n",
+      "Statistic2 is:  -131.47980446592499\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"Statistic1 is: \", statistic1)\n",
+    "print(\"Statistic2 is: \", statistic2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 63,
+   "id": "16b21ac4-d88c-4537-88b1-286d099fe4c3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "result_nm = norm.rvs(loc=sample_mean1, scale=sample_std1, size=n1)\n",
+    "result_om = norm.rvs(loc=sample_mean2, scale=sample_std2, size=n2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "id": "4f263201-4c2d-4c8f-b6c6-00738823dbf2",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[41.16912636 42.7804341  41.83049697 41.84900104 41.42524585 43.18153511\n",
+      " 41.865567   42.40788018 42.23398789 42.2897537 ] \n",
+      "\n",
+      "[41.1795803  42.57820968 43.8178388  42.7216277  42.59886934 44.33333382\n",
+      " 43.12462427 44.19597322 42.80296527 42.53386869]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(result_nm, \"\\n\")\n",
+    "print(result_om)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 66,
+   "id": "b209d0ad-0fc1-4871-8622-e829c12d7229",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "We accept the null hypothesis because: Ttest_indResult(statistic=-2.5130521559851178, pvalue=0.021710467320837187).\n",
+      "And we can say with high level of confidence that we have enough evidence to consider the null hypothesis.\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(f\"We accept the null hypothesis because: {ttest_ind(result_nm, result_om)}.\")\n",
+    "print(\"And we can say with high level of confidence that we have enough evidence to consider the null hypothesis.\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "501614ae",
+   "metadata": {},
+   "source": [
+    "## 2. An additional problem (not mandatory): In this case we can't assume that the population variances are equal. Hence in this case we cannot pool the variances.\n",
+    "   Independent random samples of 17 sophomores and 13 juniors attending a large university yield the following data on grade point averages. Data is provided in the file `files_for_lab/student_gpa.txt`.\n",
+    "   At the 5% significance level, do the data provide sufficient evidence to conclude that the mean GPAs of sophomores and juniors at the university differ?\n",
+    "\n",
+    "   Test statistics can be calculated as: [link to the image - Test statistics calculation for Unpooled Variance Case](https://education-team-2020.s3-eu-west-1.amazonaws.com/data-analytics/7.04/7.04-unpooled_variances.png)\n",
+    "\n",
+    "   Degrees of freedom is `(n1-1)+(n2-1)`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "3925f57e",
+   "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>sophomores</th>\n",
+       "      <th>juniors</th>\n",
+       "      <th>Unnamed: 2</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>3.04</td>\n",
+       "      <td>2.56</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>1.71</td>\n",
+       "      <td>2.77</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>3.30</td>\n",
+       "      <td>2.70</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>2.88</td>\n",
+       "      <td>3.00</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>2.11</td>\n",
+       "      <td>2.98</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>5</th>\n",
+       "      <td>2.60</td>\n",
+       "      <td>3.47</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>6</th>\n",
+       "      <td>2.92</td>\n",
+       "      <td>3.26</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>7</th>\n",
+       "      <td>3.60</td>\n",
+       "      <td>3.20</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>8</th>\n",
+       "      <td>2.28</td>\n",
+       "      <td>3.19</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>9</th>\n",
+       "      <td>2.82</td>\n",
+       "      <td>2.65</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>10</th>\n",
+       "      <td>3.03</td>\n",
+       "      <td>3.00</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>11</th>\n",
+       "      <td>3.13</td>\n",
+       "      <td>3.39</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>12</th>\n",
+       "      <td>2.86</td>\n",
+       "      <td>2.58</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>13</th>\n",
+       "      <td>3.49</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>14</th>\n",
+       "      <td>3.11</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>15</th>\n",
+       "      <td>2.13</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>16</th>\n",
+       "      <td>3.27</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "    sophomores  juniors  Unnamed: 2\n",
+       "0         3.04     2.56         NaN\n",
+       "1         1.71     2.77         NaN\n",
+       "2         3.30     2.70         NaN\n",
+       "3         2.88     3.00         NaN\n",
+       "4         2.11     2.98         NaN\n",
+       "5         2.60     3.47         NaN\n",
+       "6         2.92     3.26         NaN\n",
+       "7         3.60     3.20         NaN\n",
+       "8         2.28     3.19         NaN\n",
+       "9         2.82     2.65         NaN\n",
+       "10        3.03     3.00         NaN\n",
+       "11        3.13     3.39         NaN\n",
+       "12        2.86     2.58         NaN\n",
+       "13        3.49      NaN         NaN\n",
+       "14        3.11      NaN         NaN\n",
+       "15        2.13      NaN         NaN\n",
+       "16        3.27      NaN         NaN"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df1 =pd.read_excel(\"/Users/spicasumampouw/IronSpica/lab/Unit_7/lab-t-tests-p-values/files_for_lab/student_gpa.xlsx\")\n",
+    "df1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "139519e0-ba6f-4487-ae93-7301f3a9991a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df1 = df1.drop(columns=\"Unnamed: 2\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "1e3ecc71-67c2-4511-978d-c8d03f96d178",
+   "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>count</th>\n",
+       "      <th>mean</th>\n",
+       "      <th>std</th>\n",
+       "      <th>min</th>\n",
+       "      <th>25%</th>\n",
+       "      <th>50%</th>\n",
+       "      <th>75%</th>\n",
+       "      <th>max</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>sophomores</th>\n",
+       "      <td>17.0</td>\n",
+       "      <td>2.840000</td>\n",
+       "      <td>0.519832</td>\n",
+       "      <td>1.71</td>\n",
+       "      <td>2.6</td>\n",
+       "      <td>2.92</td>\n",
+       "      <td>3.13</td>\n",
+       "      <td>3.60</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>juniors</th>\n",
+       "      <td>13.0</td>\n",
+       "      <td>2.980769</td>\n",
+       "      <td>0.309259</td>\n",
+       "      <td>2.56</td>\n",
+       "      <td>2.7</td>\n",
+       "      <td>3.00</td>\n",
+       "      <td>3.20</td>\n",
+       "      <td>3.47</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "            count      mean       std   min  25%   50%   75%   max\n",
+       "sophomores   17.0  2.840000  0.519832  1.71  2.6  2.92  3.13  3.60\n",
+       "juniors      13.0  2.980769  0.309259  2.56  2.7  3.00  3.20  3.47"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df1.describe().T"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "338b9c92-043a-4997-a1ba-b98742bf03da",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sample_mean_ex1 = df1[\"sophomores\"].mean()\n",
+    "sample_mean_ex2 = df1[\"juniors\"].mean()\n",
+    "sample_std_ex1 = df1[\"sophomores\"].std()\n",
+    "sample_std_ex2 = df1[\"juniors\"].std()\n",
+    "n_ex1 = len(df1[\"sophomores\"])\n",
+    "n_ex2 = len(df1[\"juniors\"])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "e5a0c297-a0b3-4881-b81c-373ae016523f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "result_s = norm.rvs(loc=sample_mean_ex1, scale=sample_std_ex1, size=n_ex1)\n",
+    "result_j = norm.rvs(loc=sample_mean_ex2, scale=sample_std_ex2, size=n_ex2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "b1e467bd-efdd-4068-b741-370875538cbe",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "We accept the null hypothesis because: Ttest_indResult(statistic=-2.0150645185024647, pvalue=0.052363606866640794).\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(f\"We accept the null hypothesis because: {ttest_ind(result_s, result_j)}.\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "65fde408-f2c3-4a46-a59d-7156d7e3868e",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "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": "3.8.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/Solutions.ipynb b/Solutions.ipynb
new file mode 100644
index 0000000..7c6e66e
--- /dev/null
+++ b/Solutions.ipynb
@@ -0,0 +1,589 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "ee314908",
+   "metadata": {},
+   "source": [
+    "# Lab | Inferential statistics - T-test & P-value"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "cafe0ae7-2c1f-4bfb-b8ce-91ec5f88a309",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "import math\n",
+    "import statistics\n",
+    "from scipy.stats import ttest_ind, norm"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "515aa25e",
+   "metadata": {},
+   "source": [
+    "## 1.  We will have another simple example on two sample t test (pooled- when the variances are equal). But this time this is a one sided t-test\n",
+    "\n",
+    "In a packing plant, a machine packs cartons with jars. It is supposed that a new machine will pack faster on the average than the machine currently used. To test that hypothesis, the times it takes each machine to pack ten cartons are recorded. The results, in seconds, are shown in the tables in the file `files_for_lab/machine.txt`.\n",
+    "Assume that there is sufficient evidence to conduct the t test, does the data provide sufficient evidence to show if one machine is better than the other\n",
+    "\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "024e25df-ad3f-41b9-9db0-d90a8cc6b12d",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "   new_machine  old_machine\n",
+      "0         42.1         42.7\n",
+      "1         41.0         43.6\n",
+      "2         41.3         43.8\n",
+      "3         41.8         43.3\n",
+      "4         42.4         42.5\n",
+      "5         42.8         43.5\n",
+      "6         43.2         43.1\n",
+      "7         42.3         41.7\n",
+      "8         41.8         44.0\n",
+      "9         42.7         44.1\n"
+     ]
+    }
+   ],
+   "source": [
+    "df = pd.read_excel('/Users/spicasumampouw/IronSpica/lab/Unit_7/lab-t-tests-p-values/files_for_lab/machine.xlsx')\n",
+    "print(df)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "c3dfe8ce-f6c7-4573-a71d-d2a88bd93068",
+   "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>count</th>\n",
+       "      <th>mean</th>\n",
+       "      <th>std</th>\n",
+       "      <th>min</th>\n",
+       "      <th>25%</th>\n",
+       "      <th>50%</th>\n",
+       "      <th>75%</th>\n",
+       "      <th>max</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>new_machine</th>\n",
+       "      <td>10.0</td>\n",
+       "      <td>42.14</td>\n",
+       "      <td>0.683455</td>\n",
+       "      <td>41.0</td>\n",
+       "      <td>41.8</td>\n",
+       "      <td>42.2</td>\n",
+       "      <td>42.625</td>\n",
+       "      <td>43.2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>old_machine</th>\n",
+       "      <td>10.0</td>\n",
+       "      <td>43.23</td>\n",
+       "      <td>0.749889</td>\n",
+       "      <td>41.7</td>\n",
+       "      <td>42.8</td>\n",
+       "      <td>43.4</td>\n",
+       "      <td>43.750</td>\n",
+       "      <td>44.1</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "             count   mean       std   min   25%   50%     75%   max\n",
+       "new_machine   10.0  42.14  0.683455  41.0  41.8  42.2  42.625  43.2\n",
+       "old_machine   10.0  43.23  0.749889  41.7  42.8  43.4  43.750  44.1"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df.describe().T"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 61,
+   "id": "f6a79e0b-0993-414a-aa32-1a1f4ea38b98",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sample_mean1 = df[\"new_machine\"].mean()\n",
+    "sample_mean2 = df[\"old_machine\"].mean()\n",
+    "sample_std1 = df[\"new_machine\"].std()\n",
+    "sample_std2 = df[\"old_machine\"].std()\n",
+    "n1 = len(df[\"new_machine\"])\n",
+    "n2 = len(df[\"old_machine\"])\n",
+    "\n",
+    "pop_mean = df[\"new_machine\"].mean()+df[\"old_machine\"].mean()\n",
+    "pop_std = df[\"new_machine\"].std()+df[\"old_machine\"].std()\n",
+    "n = len(df[\"new_machine\"])+len(df[\"old_machine\"])\n",
+    "\n",
+    "statistic1 = (sample_mean1 - pop_mean)/(pop_std/math.sqrt(n))\n",
+    "statistic2 = (sample_mean2 - pop_mean)/(pop_std/math.sqrt(n))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 62,
+   "id": "2ce0f7f1-7792-4e04-ad59-3360fcf187df",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Statistic1 is:  -134.8806821799226\n",
+      "Statistic2 is:  -131.47980446592499\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"Statistic1 is: \", statistic1)\n",
+    "print(\"Statistic2 is: \", statistic2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 63,
+   "id": "16b21ac4-d88c-4537-88b1-286d099fe4c3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "result_nm = norm.rvs(loc=sample_mean1, scale=sample_std1, size=n1)\n",
+    "result_om = norm.rvs(loc=sample_mean2, scale=sample_std2, size=n2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "id": "4f263201-4c2d-4c8f-b6c6-00738823dbf2",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[41.16912636 42.7804341  41.83049697 41.84900104 41.42524585 43.18153511\n",
+      " 41.865567   42.40788018 42.23398789 42.2897537 ] \n",
+      "\n",
+      "[41.1795803  42.57820968 43.8178388  42.7216277  42.59886934 44.33333382\n",
+      " 43.12462427 44.19597322 42.80296527 42.53386869]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(result_nm, \"\\n\")\n",
+    "print(result_om)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 66,
+   "id": "b209d0ad-0fc1-4871-8622-e829c12d7229",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "We accept the null hypothesis because: Ttest_indResult(statistic=-2.5130521559851178, pvalue=0.021710467320837187).\n",
+      "And we can say with high level of confidence that we have enough evidence to consider the null hypothesis.\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(f\"We accept the null hypothesis because: {ttest_ind(result_nm, result_om)}.\")\n",
+    "print(\"And we can say with high level of confidence that we have enough evidence to consider the null hypothesis.\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "501614ae",
+   "metadata": {},
+   "source": [
+    "## 2. An additional problem (not mandatory): In this case we can't assume that the population variances are equal. Hence in this case we cannot pool the variances.\n",
+    "   Independent random samples of 17 sophomores and 13 juniors attending a large university yield the following data on grade point averages. Data is provided in the file `files_for_lab/student_gpa.txt`.\n",
+    "   At the 5% significance level, do the data provide sufficient evidence to conclude that the mean GPAs of sophomores and juniors at the university differ?\n",
+    "\n",
+    "   Test statistics can be calculated as: [link to the image - Test statistics calculation for Unpooled Variance Case](https://education-team-2020.s3-eu-west-1.amazonaws.com/data-analytics/7.04/7.04-unpooled_variances.png)\n",
+    "\n",
+    "   Degrees of freedom is `(n1-1)+(n2-1)`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "3925f57e",
+   "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>sophomores</th>\n",
+       "      <th>juniors</th>\n",
+       "      <th>Unnamed: 2</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>3.04</td>\n",
+       "      <td>2.56</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>1.71</td>\n",
+       "      <td>2.77</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>3.30</td>\n",
+       "      <td>2.70</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>2.88</td>\n",
+       "      <td>3.00</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>2.11</td>\n",
+       "      <td>2.98</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>5</th>\n",
+       "      <td>2.60</td>\n",
+       "      <td>3.47</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>6</th>\n",
+       "      <td>2.92</td>\n",
+       "      <td>3.26</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>7</th>\n",
+       "      <td>3.60</td>\n",
+       "      <td>3.20</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>8</th>\n",
+       "      <td>2.28</td>\n",
+       "      <td>3.19</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>9</th>\n",
+       "      <td>2.82</td>\n",
+       "      <td>2.65</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>10</th>\n",
+       "      <td>3.03</td>\n",
+       "      <td>3.00</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>11</th>\n",
+       "      <td>3.13</td>\n",
+       "      <td>3.39</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>12</th>\n",
+       "      <td>2.86</td>\n",
+       "      <td>2.58</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>13</th>\n",
+       "      <td>3.49</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>14</th>\n",
+       "      <td>3.11</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>15</th>\n",
+       "      <td>2.13</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>16</th>\n",
+       "      <td>3.27</td>\n",
+       "      <td>NaN</td>\n",
+       "      <td>NaN</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "    sophomores  juniors  Unnamed: 2\n",
+       "0         3.04     2.56         NaN\n",
+       "1         1.71     2.77         NaN\n",
+       "2         3.30     2.70         NaN\n",
+       "3         2.88     3.00         NaN\n",
+       "4         2.11     2.98         NaN\n",
+       "5         2.60     3.47         NaN\n",
+       "6         2.92     3.26         NaN\n",
+       "7         3.60     3.20         NaN\n",
+       "8         2.28     3.19         NaN\n",
+       "9         2.82     2.65         NaN\n",
+       "10        3.03     3.00         NaN\n",
+       "11        3.13     3.39         NaN\n",
+       "12        2.86     2.58         NaN\n",
+       "13        3.49      NaN         NaN\n",
+       "14        3.11      NaN         NaN\n",
+       "15        2.13      NaN         NaN\n",
+       "16        3.27      NaN         NaN"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df1 =pd.read_excel(\"/Users/spicasumampouw/IronSpica/lab/Unit_7/lab-t-tests-p-values/files_for_lab/student_gpa.xlsx\")\n",
+    "df1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "139519e0-ba6f-4487-ae93-7301f3a9991a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df1 = df1.drop(columns=\"Unnamed: 2\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "1e3ecc71-67c2-4511-978d-c8d03f96d178",
+   "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>count</th>\n",
+       "      <th>mean</th>\n",
+       "      <th>std</th>\n",
+       "      <th>min</th>\n",
+       "      <th>25%</th>\n",
+       "      <th>50%</th>\n",
+       "      <th>75%</th>\n",
+       "      <th>max</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>sophomores</th>\n",
+       "      <td>17.0</td>\n",
+       "      <td>2.840000</td>\n",
+       "      <td>0.519832</td>\n",
+       "      <td>1.71</td>\n",
+       "      <td>2.6</td>\n",
+       "      <td>2.92</td>\n",
+       "      <td>3.13</td>\n",
+       "      <td>3.60</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>juniors</th>\n",
+       "      <td>13.0</td>\n",
+       "      <td>2.980769</td>\n",
+       "      <td>0.309259</td>\n",
+       "      <td>2.56</td>\n",
+       "      <td>2.7</td>\n",
+       "      <td>3.00</td>\n",
+       "      <td>3.20</td>\n",
+       "      <td>3.47</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "            count      mean       std   min  25%   50%   75%   max\n",
+       "sophomores   17.0  2.840000  0.519832  1.71  2.6  2.92  3.13  3.60\n",
+       "juniors      13.0  2.980769  0.309259  2.56  2.7  3.00  3.20  3.47"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df1.describe().T"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "338b9c92-043a-4997-a1ba-b98742bf03da",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sample_mean_ex1 = df1[\"sophomores\"].mean()\n",
+    "sample_mean_ex2 = df1[\"juniors\"].mean()\n",
+    "sample_std_ex1 = df1[\"sophomores\"].std()\n",
+    "sample_std_ex2 = df1[\"juniors\"].std()\n",
+    "n_ex1 = len(df1[\"sophomores\"])\n",
+    "n_ex2 = len(df1[\"juniors\"])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "e5a0c297-a0b3-4881-b81c-373ae016523f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "result_s = norm.rvs(loc=sample_mean_ex1, scale=sample_std_ex1, size=n_ex1)\n",
+    "result_j = norm.rvs(loc=sample_mean_ex2, scale=sample_std_ex2, size=n_ex2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "b1e467bd-efdd-4068-b741-370875538cbe",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "We accept the null hypothesis because: Ttest_indResult(statistic=-2.0150645185024647, pvalue=0.052363606866640794).\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(f\"We accept the null hypothesis because: {ttest_ind(result_s, result_j)}.\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "65fde408-f2c3-4a46-a59d-7156d7e3868e",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "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": "3.8.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/Untitled.ipynb b/Untitled.ipynb
deleted file mode 100644
index bb907ae..0000000
--- a/Untitled.ipynb
+++ /dev/null
@@ -1,76 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "ee314908",
-   "metadata": {},
-   "source": [
-    "# Lab | Inferential statistics - T-test & P-value"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "515aa25e",
-   "metadata": {},
-   "source": [
-    "## 1.  We will have another simple example on two sample t test (pooled- when the variances are equal). But this time this is a one sided t-test\n",
-    "\n",
-    "In a packing plant, a machine packs cartons with jars. It is supposed that a new machine will pack faster on the average than the machine currently used. To test that hypothesis, the times it takes each machine to pack ten cartons are recorded. The results, in seconds, are shown in the tables in the file `files_for_lab/machine.txt`.\n",
-    "Assume that there is sufficient evidence to conduct the t test, does the data provide sufficient evidence to show if one machine is better than the other\n",
-    "\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "c4797fc7",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "markdown",
-   "id": "501614ae",
-   "metadata": {},
-   "source": [
-    "## 2. An additional problem (not mandatory): In this case we can't assume that the population variances are equal. Hence in this case we cannot pool the variances.\n",
-    "   Independent random samples of 17 sophomores and 13 juniors attending a large university yield the following data on grade point averages. Data is provided in the file `files_for_lab/student_gpa.txt`.\n",
-    "   At the 5% significance level, do the data provide sufficient evidence to conclude that the mean GPAs of sophomores and juniors at the university differ?\n",
-    "\n",
-    "   Test statistics can be calculated as: [link to the image - Test statistics calculation for Unpooled Variance Case](https://education-team-2020.s3-eu-west-1.amazonaws.com/data-analytics/7.04/7.04-unpooled_variances.png)\n",
-    "\n",
-    "   Degrees of freedom is `(n1-1)+(n2-1)`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "3925f57e",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "ironhack",
-   "language": "python",
-   "name": "ironhack"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.8.5"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/files_for_lab/machine.txt b/files_for_lab/machine.txt
index b26c8d4..34fc1ec 100644
Binary files a/files_for_lab/machine.txt and b/files_for_lab/machine.txt differ
diff --git a/files_for_lab/machine.xlsx b/files_for_lab/machine.xlsx
new file mode 100644
index 0000000..f4ba5e3
Binary files /dev/null and b/files_for_lab/machine.xlsx differ
diff --git a/files_for_lab/student_gpa.txt b/files_for_lab/student_gpa.txt
index ad44343..455af2d 100644
--- a/files_for_lab/student_gpa.txt
+++ b/files_for_lab/student_gpa.txt
@@ -1,18 +1,18 @@
-Sophomores	  Juniors
-3.04	        2.56
-1.71	        2.77
-3.3	          2.7
-2.88	        3
-2.11	        2.98
-2.6	          3.47
-2.92	        3.26
-3.6	          3.2
-2.28	        3.19
-2.82	        2.65
-3.03	        3
-3.13	        3.39
-2.86	        2.58
-3.49	
-3.11	
-2.13	
-3.27
+Sophomores     Juniors
+3,04	        2,56
+1,71	        2,77
+3,3	        2,7
+2,88	        3
+2,11	        2,98
+2,6	        3,47
+2,92	        3,26
+3,6	        3,2
+2,28	        3,19
+2,82	        2,65
+3,03	        3
+3,13	        3,39
+2,86	        2,58
+3,49	
+3,11	
+2,13	
+3,27
diff --git a/files_for_lab/student_gpa.xlsx b/files_for_lab/student_gpa.xlsx
new file mode 100644
index 0000000..30e6f0f
Binary files /dev/null and b/files_for_lab/student_gpa.xlsx differ