From 0cd2e1ab33174a432abdcd809f6f94da50099dd7 Mon Sep 17 00:00:00 2001
From: Dulce-04 <136611956+Dulce-04@users.noreply.github.com>
Date: Fri, 11 Aug 2023 15:28:12 +0100
Subject: [PATCH] Confidence Intervals

---
 your-code/main.ipynb | 153 +++++++++++++++++++++++++++++++++++++------
 1 file changed, 134 insertions(+), 19 deletions(-)

diff --git a/your-code/main.ipynb b/your-code/main.ipynb
index 332f496..b66b54c 100644
--- a/your-code/main.ipynb
+++ b/your-code/main.ipynb
@@ -9,11 +9,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [],
    "source": [
-    "# Libraries"
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "import scipy.stats as st"
    ]
   },
   {
@@ -32,11 +34,29 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 6,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(172.14308590115726, 174.79024743217607)"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
-    "# your code here"
+    "heights = [167, 167, 168, 168, 168, 169, 171, 172, 173, 175, 175, 175, 177, 182, 195]\n",
+    "\n",
+    "mean = np.mean(heights)\n",
+    "alpha = 0.80\n",
+    "std = 4\n",
+    "n = len(heights)\n",
+    "\n",
+    "st.norm.interval(0.80, loc=mean, scale=std/np.sqrt(n))"
    ]
   },
   {
@@ -51,11 +71,82 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 10,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(0.2463369513350275, 0.2679487629506867)"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
-    "# your code here"
+    "sample_size = 105\n",
+    "losses = 27\n",
+    "n = 105\n",
+    "\n",
+    "p = losses/ sample_size\n",
+    "\n",
+    "z_value = st.norm.ppf(1 - (0.80)/2)\n",
+    "\n",
+    "margin_of_error = z_value * np.sqrt((p * (1 - p))/n)\n",
+    "\n",
+    "lower_bound = p - margin_of_error\n",
+    "upper_bound = p + margin_of_error\n",
+    "\n",
+    "print(f'Our CI for proportion is [{lower_bound}, {upper_bound}]')\n",
+    "\n",
+    "st.norm.interval(1 - confidence_level_80, loc= mean, scale=std / np.sqrt(n))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Our CI for proportion is [0.25178307737433503, 0.2625026369113792]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(173.4176134996416, 173.51571983369175)"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sample_size = 105\n",
+    "losses = 27\n",
+    "n = 105\n",
+    "\n",
+    "p = losses/ sample_size\n",
+    "\n",
+    "z_value = st.norm.ppf(1 - (0.90)/2)\n",
+    "\n",
+    "se = np.sqrt((p * (1 - p))/n)     \n",
+    "\n",
+    "margin_of_error = z_value * se\n",
+    "\n",
+    "lower_bound = p - margin_of_error\n",
+    "upper_bound = p + margin_of_error\n",
+    "\n",
+    "print(f'Our CI for proportion is [{lower_bound}, {upper_bound}]')\n",
+    "\n",
+    "confidence_level_90 = 0.90\n",
+    "st.norm.interval(1 - confidence_level_90, loc= mean, scale=std / np.sqrt(n))"
    ]
   },
   {
@@ -76,11 +167,23 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 23,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2.0537489106318225"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
-    "# your code here"
+    "z = st.norm.ppf(0.98)  \n",
+    "z"
    ]
   },
   {
@@ -94,11 +197,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 21,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Sample Size: 4106\n"
+     ]
+    }
+   ],
    "source": [
-    "# your code here"
+    "confidence_level = 0.80\n",
+    "desired_error = 0.01 \n",
+    "\n",
+    "z_alpha_over_2 = stats.norm.ppf(1 - (1 - confidence_level) / 2)\n",
+    "\n",
+    "sample_size = ((z_alpha_over_2**2 * 0.5 * 0.5) / desired_error**2)\n",
+    "print(\"Sample Size:\", round(sample_size))"
    ]
   },
   {
@@ -124,14 +241,12 @@
    "execution_count": null,
    "metadata": {},
    "outputs": [],
-   "source": [
-    "# your code here"
-   ]
+   "source": []
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -145,7 +260,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.3"
+   "version": "3.10.9"
   }
  },
  "nbformat": 4,