[Python] need help on z test , t test, and regreesion

import numpy as np from statsmodels.stats.weightstats import ztest import matplotlib.pyplot as plt import seaborn as sns from scipy import stats

def perform_one_sample_z_test(sample_data, population_mean_hypothesized, population_std, alpha=0.05): """ Performs a one-sample Z-test.

Args:
sample_data (array-like): The sample observations.
population_mean_hypothesized (float): The hypothesized population mean (mu_0).
population_std (float): The known population standard deviation (sigma).
alpha (float): The significance level (default is 0.05).

Returns:
tuple: A tuple containing:
- z_statistic (float): The calculated Z-statistic.
- p_value (float): The p-value from the Z-test.
- interpretation (str): A string interpreting the results.
"""
sample_mean = np.mean(sample_data)
n = len(sample_data)

print(f"--- One-Sample Z-Test ---")
print(f"Sample Size (n): {n}")
print(f"Sample Mean: {sample_mean:.4f}")
print(f"Hypothesized Population Mean (μ₀): {population_mean_hypothesized}")
print(f"Known Population Standard Deviation (σ): {population_std}")
print(f"Significance Level (α): {alpha}")

# Perform the Z-test
# The 'value' parameter in ztest is the hypothesized population mean
# 'ddof=0' for population standard deviation (n-0 in denominator for std calc if used from sample, but here we provide known pop_std)
# The default 'alternative' is 'two-sided'
z_statistic, p_value = ztest(x1=sample_data, value=population_mean_hypothesized, ddof=0, x2=None)

interpretation = ""
if p_value < alpha:
interpretation = (f"Since the p-value ({p_value:.4f}) is less than alpha ({alpha}), "
"we reject the null hypothesis.\n"
"Conclusion: There is statistically significant evidence that the sample mean "
f"({sample_mean:.4f}) is significantly different from the hypothesized population mean "
f"({population_mean_hypothesized}).")
else:
interpretation = (f"Since the p-value ({p_value:.4f}) is greater than or equal to alpha ({alpha}), "
"we fail to reject the null hypothesis.\n"
"Conclusion: There is no statistically significant evidence to suggest that the sample mean "
f"({sample_mean:.4f}) is significantly different from the hypothesized population mean "
f"({population_mean_hypothesized}).")

print(f"\nZ-statistic: {z_statistic:.4f}")
print(f"P-value: {p_value:.4f}")
print(interpretation)

return z_statistic, p_value, interpretation

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