From 6e29e806087770d160981f3c2da39d92b87c647d Mon Sep 17 00:00:00 2001
From: Sergio Soutinho <sergio.soutinho@gmail.com>
Date: Fri, 11 Aug 2023 15:27:01 +0100
Subject: [PATCH] lab done

---
 your-code/main.ipynb | 142 ++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 133 insertions(+), 9 deletions(-)

diff --git a/your-code/main.ipynb b/your-code/main.ipynb
index 332f496..dea2b22 100644
--- a/your-code/main.ipynb
+++ b/your-code/main.ipynb
@@ -9,11 +9,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
-    "# Libraries"
+    "# Libraries\n",
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "import scipy.stats as st"
    ]
   },
   {
@@ -30,13 +33,68 @@
     "**Hint**: function `stats.norm.interval` from `scipy` can help you get through this exercise. "
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "st.norm.interval - we use when we know the std of the population and n~of observation is greater than 30\n",
+    "st.t.interval - when we dont know the std of the population or nº of observation is less than 30"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(172.14308590115726, 174.79024743217607)"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
-    "# your code here"
+    "# your code here\n",
+    "# NORM DIST\n",
+    "\n",
+    "heights = [167, 167, 168, 168, 168, 169, 171, 172, 173, 175, 175, 175, 177, 182, 195]\n",
+    "alpha = 0.80\n",
+    "std = 4\n",
+    "mean = np.mean(heights)\n",
+    "n = len(heights)\n",
+    "\n",
+    "st.norm.interval(0.80, loc = mean, scale = std/np.sqrt(n))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(170.9117270472475, 176.02160628608584)"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# doing with T\n",
+    "\n",
+    "heights = np.array([167, 167, 168, 168, 168, 169, 171, 172, 173, 175, 175, 175, 177, 182, 195])\n",
+    "s = heights.std(ddof=1)\n",
+    "mean = heights.mean()\n",
+    "n = len(heights)\n",
+    "\n",
+    "st.t.interval(0.80, n-1, loc = mean, scale = s/np.sqrt(n))"
    ]
   },
   {
@@ -51,11 +109,77 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 16,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "80%:  [0.20248138545542083, 0.3118043288302934]\n",
+      "90%:  [0.18698561776452813, 0.3273000965211861]\n"
+     ]
+    }
+   ],
    "source": [
-    "# your code here"
+    "n = 105\n",
+    "losses = 27\n",
+    "p = losses / n\n",
+    "\n",
+    "z80 = st.norm.ppf(1-(1-0.8)/2)\n",
+    "moe80 = z80 * np.sqrt((p*(1-p))/n)\n",
+    "\n",
+    "\n",
+    "z90 = st.norm.ppf(1-(1-0.9)/2)\n",
+    "moe90 = z90 * np.sqrt((p*(1-p))/n)\n",
+    "\n",
+    "\n",
+    "CI80 = [p-moe80, p+moe80]\n",
+    "CI90 = [p-moe90, p+moe90]\n",
+    "print(\"80%: \", CI80)\n",
+    "print(\"90%: \", CI90)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(0.20248138545542083, 0.3118043288302934)"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# PYTHON WAY\n",
+    "st.norm.interval(0.80, loc = p, scale = np.sqrt((p*(1-p))/n))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(0.1869856177645281, 0.3273000965211861)"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# PYTHON WAY\n",
+    "st.norm.interval(0.90, loc = p, scale = np.sqrt((p*(1-p))/n))"
    ]
   },
   {
@@ -145,7 +269,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.3"
+   "version": "3.10.9"
   }
  },
  "nbformat": 4,