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[lab-goodfit-indeptests]AnaCarvalho #159

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152 changes: 142 additions & 10 deletions your_code/main.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -14,11 +14,47 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 15,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Chi-squared statistic: 6.491310681109821\n",
"P-value: 0.4836889068537269\n",
"Fail to reject the null hypothesis: The data follows a Poisson distribution.\n"
]
}
],
"source": [
"# your answer here"
"import pandas as pd\n",
"import numpy as np\n",
"import scipy.stats as st\n",
"\n",
"from scipy.stats import poisson\n",
"\n",
"significance = 0.05\n",
"mu = 2.435\n",
"f_obs = np.array([35, 99, 104, 110, 62, 25, 10, 3])\n",
"poisson_dist = poisson(mu)\n",
"\n",
"poisson_pmfs = np.array([poisson_dist.pmf(i) for i in range(0, 7)])\n",
"poisson_pmfs_last = np.append(poisson_pmfs, 1 - poisson_pmfs.sum())\n",
"f_exp = poisson_pmfs_last * 448\n",
"\n",
"# Perform the chi-squared goodness-of-fit test\n",
"chi_squared, p_value = st.chisquare(f_obs=f_obs, f_exp=f_exp)\n",
"\n",
"# Compare p-value with significance level\n",
"if p_value < significance:\n",
" result = \"Reject the null hypothesis: The data does not follow a Poisson distribution.\"\n",
"else:\n",
" result = \"Fail to reject the null hypothesis: The data follows a Poisson distribution.\"\n",
"\n",
"print(\"Chi-squared statistic:\", chi_squared)\n",
"print(\"P-value:\", p_value)\n",
"print(result)"
]
},
{
Expand All @@ -41,7 +77,7 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
Expand All @@ -60,11 +96,59 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 17,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"We can reject the null hypothesis\n",
"p-value: 0.015715783395950887\n"
]
}
],
"source": [
"# your answer here"
"from scipy.stats import binom\n",
"\n",
"# H0: The sample comes from a binomial population (with n = 10 and p = 0.05)\n",
"# H1: The sample does not come from a binomial population (with n = 10 and p = 0.05)\n",
"\n",
"# Observed frequencies of defective tires\n",
"O = np.array([138, 53, 9])\n",
"\n",
"population = O.sum()\n",
"n = 10\n",
"p = 0.05\n",
"alpha = 0.05 \n",
"\n",
"binom_dist = binom(n, p)\n",
"\n",
"\n",
"# Calculate the entire PMF for 0 to 2 or more\n",
"binom_pmfs = np.array([binom_dist.pmf(i) for i in range(0, 2)])\n",
"\n",
"tail = 1 - binom_pmfs.sum()\n",
"\n",
"binom_with_tail = np.append(binom_pmfs, tail)\n",
"\n",
"E = binom_with_tail * population\n",
"\n",
"chisquare_result = st.chisquare(f_obs = O, f_exp = E)\n",
"\n",
"if chisquare_result.pvalue < alpha:\n",
" print(\"We can reject the null hypothesis\")\n",
"else:\n",
" print(\"We can not reject the null hypothesis\")\n",
" \n",
"print(\"p-value:\", chisquare_result.pvalue)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Since this p-value is less than the chosen significance level (alpha = 0.05), i can reject the null hypothesis. This suggests that there is evidence to believe that the observed data does not follow a binomial distribution.The result indicates that the distribution of defective tires in the sample significantly deviates from what would be expected under the assumed binomial distribution."
]
},
{
Expand All @@ -79,11 +163,59 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 18,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Chi-squared statistic: 10.712198008709638\n",
"P-value: 0.004719280137040844\n",
"Degrees of freedom: 2\n",
"Expected frequencies:\n",
" [[24.08421053 19.91578947]\n",
" [19.70526316 16.29473684]\n",
" [ 8.21052632 6.78947368]]\n",
"We can reject the null hypothesis\n"
]
}
],
"source": [
"from scipy.stats import chi2_contingency\n",
"\n",
"#Hypothesis\n",
"\n",
"#H0 : Physical Activity is independent of sugar drinks consumption \n",
"#H1 : Physical Activity is not independent of sugar drinks consumption\n",
"\n",
"alpha = 0.05\n",
"\n",
"\n",
"children = [[32, 12],\n",
" [14, 22],\n",
" [6,9]]\n",
"\n",
"chi2_stat, p_val, dof, expected = chi2_contingency(children)\n",
"\n",
"print(\"Chi-squared statistic:\", chi2_stat)\n",
"print(\"P-value:\", p_val)\n",
"print(\"Degrees of freedom:\", dof)\n",
"print(\"Expected frequencies:\\n\", expected)\n",
"\n",
"if p_val < alpha:\n",
" print(\"We can reject the null hypothesis\")\n",
"else:\n",
" print(\"We cannot reject the null hypothesis\")"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"#your answer here"
"#The rejection of the null hypothesis suggests that there might be a meaningful connection between physical activity and sugar drinks consumption"
]
}
],
Expand All @@ -103,7 +235,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.3"
"version": "3.10.9"
}
},
"nbformat": 4,
Expand Down