Python uses Statsmodes for hypothesis testing and confidence interval estimation, including single sample test, double sample test, analysis of variance, Chi-squared test, t test, etc

Firstly, in order to use Statsmodes for hypothesis testing and confidence interval estimation, we need to install the Statsmodes library in Python. You can install using the following command: pip install statsmodels Statsmodes is a Python library for implementing statistical models and data exploration. In this example, we will use different modules in Statsmodes to perform different types of hypothesis testing and confidence interval estimation. Next, we will introduce the usage of each module in Statsmodes and provide corresponding examples and complete Python code. 1. Single sample inspection Single sample testing is used to compare the difference between the mean of a sample and the expected theoretical mean. Example code: python import numpy as np from statsmodels.stats import weightstats as stests #Sample data sample_data = np.array([5, 6, 7, 8, 9]) #Single sample t-test t_stat, p_value, _ = stests.ztest(sample_data, value=10) Print ("t statistic:", t-stat) Print ("p-value:", p-value) 2. Double sample test The double sample test is used to compare the differences between the means of two samples. Example code: python import numpy as np from statsmodels.stats import weightstats as stests #Sample data sample_data1 = np.array([5, 6, 7, 8, 9]) sample_data2 = np.array([10, 11, 12, 13, 14]) #Double sample t-test t_stat, p_value, _ = stests.ttest_ind(sample_data1, sample_data2) Print ("t statistic:", t-stat) Print ("p-value:", p-value) 3. Analysis of variance Analysis of variance is used to compare the differences between the means of multiple samples. Example code: python import numpy as np from statsmodels.stats.anova import anova_lm #Sample data sample_data1 = np.array([5, 6, 7, 8, 9]) sample_data2 = np.array([10, 11, 12, 13, 14]) sample_data3 = np.array([15, 16, 17, 18, 19]) #Analysis of variance f_stat, p_value = anova_lm(sample_data1, sample_data2, sample_data3) Print ("F statistic:", f_stat) Print ("p-value:", p-value) 4. Chi-squared test The Chi-squared test is used to compare the difference between the observation frequency and the expected frequency. Example code: python import numpy as np from statsmodels.stats import contingency_tables #Sample data observed = np.array([[10, 20], [30, 40]]) expected = np.array([[15, 15], [25, 45]]) #Chi-squared test chi2_stat, p_value, _ = contingency_tables.chi2_contingency(observed, expected) Print ("chi square statistic:", chi2stat) Print ("p-value:", p-value) The above is a basic application example of Statsmodes library for hypothesis testing and confidence interval estimation in Python. According to the specific problem to be analyzed, different functions and modules can be selected to perform corresponding statistical analysis.