{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here's Allen Downey's article: http://allendowney.blogspot.fr/2011/08/jimmy-nut-company-problem.html"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"> “Jimmy Nut Company advertises that their nut mix contains 40% cashews, 15% brazil nuts, 20% almonds, and only 25% peanuts. The truth in advertising investigators took a random sample (of size 20 lb) of the nut mix and found the distribution to be as follows:\n",
"\n",
">Cashews Brazil Nuts Almonds Peanuts\n",
"\n",
">6 lb 3 lb 5 lb 6 lb\n",
"\n",
">At the 0.01 level of significance, is the claim made by Jimmy Nuts true?”"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"weights = {'Cashew': (16+18)/2, \n",
" 'Brazil nut': (6+8)/2, \n",
" 'Almonds': (20+24)/2, \n",
" 'Peanuts': 28.}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Converting from weight in the sample to count per ounce."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def ConvertToCount(sample, count_per):\n",
" \"\"\"Convert from weight to count.\n",
"\n",
" sample: Hist that maps from category to weight in pounds\n",
" count_per: dict that maps from category to count per ounce\n",
" \"\"\"\n",
" for value, count in sample.Items():\n",
" sample.Mult(value, 16 * count_per[value])"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"sample = dict(cashew=6, brazil=3, almond=5, peanut=6)\n",
"count_per = dict(cashew=17, brazil=7, \n",
" almond=22, peanut=28)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'almond': 22, 'brazil': 7, 'cashew': 17, 'peanut': 28}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"count_per"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"from thinkstats2 import MakeHistFromDict, MakePmfFromDict\n",
"\n",
"observed = MakeHistFromDict(sample)\n",
"ConvertToCount(observed, count_per)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Hist({'cashew': 1632, 'brazil': 336, 'almond': 1760, 'peanut': 2688})"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"observed"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"advertised = dict(cashew=40, brazil=15, \n",
" almond=20, peanut=25)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"expected = MakePmfFromDict(advertised)\n",
"ConvertToCount(expected, count_per)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Pmf({'cashew': 108.80000000000001, 'brazil': 16.8, 'almond': 70.4, 'peanut': 112.0})"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"expected"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"308.0"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"expected.Normalize(observed.Total())"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Pmf({'cashew': 2266.431168831169, 'brazil': 349.9636363636364, 'almond': 1466.514285714286, 'peanut': 2333.090909090909})"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"expected"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" expected | \n",
" observed | \n",
" error | \n",
"
\n",
" \n",
" \n",
" \n",
" | almond | \n",
" 1466.514286 | \n",
" 1760.0 | \n",
" 20.012469 | \n",
"
\n",
" \n",
" | brazil | \n",
" 349.963636 | \n",
" 336.0 | \n",
" -3.990025 | \n",
"
\n",
" \n",
" | cashew | \n",
" 2266.431169 | \n",
" 1632.0 | \n",
" -27.992519 | \n",
"
\n",
" \n",
" | peanut | \n",
" 2333.090909 | \n",
" 2688.0 | \n",
" 15.211970 | \n",
"
\n",
" \n",
"
\n",
"