[lab-inferential-statistics] Spica

.ipynb_checkpoints/ReadME-checkpoint.md

@@ -0,0 +1,18 @@
+![logo_ironhack_blue 7](https://user-images.githubusercontent.com/23629340/40541063-a07a0a8a-601a-11e8-91b5-2f13e4e6b441.png)
+
+# Lab | Inferential statistics
+
+
+### Instructions
+
+1. It is assumed that the mean systolic blood pressure is `μ = 120 mm Hg`. In the Honolulu Heart Study, a sample of `n = 100` people had an average systolic blood pressure of 130.1 mm Hg with a standard deviation of 21.21 mm Hg. Is the group significantly different (with respect to systolic blood pressure!) from the regular population?
+
+   - Set up the hypothesis test.
+   - Write down all the steps followed for setting up the test.
+   - Calculate the test statistic by hand and also code it in Python. It should be 4.76190. We will take a look at how to make decisions based on this calculated value.
+
+2. If you finished the previous question, please go through the code for `principal_component_analysis_example` provided in the `files_for_lab` folder .
+
+
+
+

.ipynb_checkpoints/Solutions-checkpoint.ipynb

@@ -0,0 +1,172 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "e00a11f1",
+   "metadata": {},
+   "source": [
+    "# Lab | Inferential statistics"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2c813f0a",
+   "metadata": {},
+   "source": [
+    "- It is assumed that the mean systolic blood pressure is `μ = 120 mm Hg`. In the Honolulu Heart Study, a sample of `n = 100` people had an average systolic blood pressure of 130.1 mm Hg with a standard deviation of 21.21 mm Hg. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "0cd42a8b-2496-4c4a-8556-e957cd80ea30",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import math"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "120875d3",
+   "metadata": {},
+   "source": [
+    "## 1. Is the group significantly different (with respect to systolic blood pressure!) from the regular population?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d26c43d4",
+   "metadata": {},
+   "source": [
+    "### 1.1 Set up the hypothesis test."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f31fb41a-fa46-42cc-ba83-11bd5b4e82d9",
+   "metadata": {},
+   "source": [
+    "- the mean systolic blood pressure is `μ = 120 mm Hg`.\n",
+    "- a sample of `n = 100`.\n",
+    "- average systolic blood pressure of `130.1 mm Hg`.\n",
+    "- standard deviation of `21.21 mm Hg`."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6b51262b",
+   "metadata": {},
+   "source": [
+    "The null hypothesis is that the mean blood pressure of people in Honolulu is not significantly different from the population mean and the alternate hypothesis is that the blood pressure of people in Honolulu is significantly different, hence we can use the Z-test to test this hypothesis."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "17c9988a",
+   "metadata": {},
+   "source": [
+    "### 1.2 Write down all the steps followed for setting up the test."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "079381b2-efeb-4942-8764-4c66d4f1f738",
+   "metadata": {},
+   "source": [
+    "- Specify the Null Hypothesis\n",
+    "- Specify the Alternative Hypothesis\n",
+    "- Set the Significance Level\n",
+    "- Calculate the Test Statistic (t | Z test) \n",
+    "- Calculate the corresponding P-Value\n",
+    "- Conclusion"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "63df3700",
+   "metadata": {},
+   "source": [
+    "### 1.3 Calculate the test statistic by hand and also code it in Python. It should be 4.76190. We will take a look at how to make decisions based on this calculated value."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "97f73e20",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The test statistic is: 4.76190\n"
+     ]
+    }
+   ],
+   "source": [
+    "sample_mean = 130.1\n",
+    "pop_mean = 120\n",
+    "sample_std = 21.21\n",
+    "n = 100\n",
+    "\n",
+    "#Z = ((130.1 - 120) / (21.21 / 10))\n",
+    "test_statistic = ( (130.1 - 120) / (21.21 / (n**0.5)) )\n",
+    "print(f\"The test statistic is: {statistic:.5f}\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "afcc7acd",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The Z test is: 4.76190\n"
+     ]
+    }
+   ],
+   "source": [
+    "sample_mean = 130.1\n",
+    "pop_mean = 120\n",
+    "sample_std = 21.21\n",
+    "n = 100\n",
+    "\n",
+    "Z = ( (sample_mean - pop_mean) / (sample_std / math.sqrt(n)) )\n",
+    "print(f\"The Z test is: {Z:.5f}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4a7564e5",
+   "metadata": {},
+   "source": [
+    "## 2. If you finished the previous question, please go through the code for principal_component_analysis_example provided in the files_for_lab folder ."
+   ]
+  }
+ ],
+ "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
+}

Solutions.ipynb

@@ -16,6 +16,16 @@
     "- It is assumed that the mean systolic blood pressure is `μ = 120 mm Hg`. In the Honolulu Heart Study, a sample of `n = 100` people had an average systolic blood pressure of 130.1 mm Hg with a standard deviation of 21.21 mm Hg. "
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "0cd42a8b-2496-4c4a-8556-e957cd80ea30",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import math"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "120875d3",
@@ -33,12 +43,23 @@
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "39c6f717",
+   "cell_type": "markdown",
+   "id": "f31fb41a-fa46-42cc-ba83-11bd5b4e82d9",
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "source": [
+    "- the mean systolic blood pressure is `μ = 120 mm Hg`.\n",
+    "- a sample of `n = 100`.\n",
+    "- average systolic blood pressure of `130.1 mm Hg`.\n",
+    "- standard deviation of `21.21 mm Hg`."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6b51262b",
+   "metadata": {},
+   "source": [
+    "The null hypothesis is that the mean blood pressure of people in Honolulu is not significantly different from the population mean and the alternate hypothesis is that the blood pressure of people in Honolulu is significantly different, hence we can use the Z-test to test this hypothesis."
+   ]
   },
   {
    "cell_type": "markdown",
@@ -49,12 +70,17 @@
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "b09ce149",
+   "cell_type": "markdown",
+   "id": "079381b2-efeb-4942-8764-4c66d4f1f738",
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "source": [
+    "- Specify the Null Hypothesis\n",
+    "- Specify the Alternative Hypothesis\n",
+    "- Set the Significance Level\n",
+    "- Calculate the Test Statistic (t | Z test) \n",
+    "- Calculate the corresponding P-Value\n",
+    "- Conclusion"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -66,11 +92,52 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 18,
    "id": "97f73e20",
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The test statistic is: 4.76190\n"
+     ]
+    }
+   ],
+   "source": [
+    "sample_mean = 130.1\n",
+    "pop_mean = 120\n",
+    "sample_std = 21.21\n",
+    "n = 100\n",
+    "\n",
+    "#Z = ((130.1 - 120) / (21.21 / 10))\n",
+    "test_statistic = ( (130.1 - 120) / (21.21 / (n**0.5)) )\n",
+    "print(f\"The test statistic is: {statistic:.5f}\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "afcc7acd",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The Z test is: 4.76190\n"
+     ]
+    }
+   ],
+   "source": [
+    "sample_mean = 130.1\n",
+    "pop_mean = 120\n",
+    "sample_std = 21.21\n",
+    "n = 100\n",
+    "\n",
+    "Z = ( (sample_mean - pop_mean) / (sample_std / math.sqrt(n)) )\n",
+    "print(f\"The Z test is: {Z:.5f}\")"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -97,7 +164,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.5"
+   "version": "3.8.8"
   }
  },
  "nbformat": 4,