Why hypothesis testing validates claims in SciPy

Introduction

Hypothesis testing helps us check if a claim about data is likely true or just happened by chance.

Checking if a new medicine works better than the old one.

Deciding if a marketing campaign increased sales.

Verifying if students' test scores improved after extra tutoring.

Determining if a machine produces fewer defects after maintenance.

Syntax

SciPy

from scipy import stats

# Example: stats.ttest_1samp(data, popmean)

# data: list or array of sample values
# popmean: the value to test against

Use stats.ttest_1samp for testing if the sample mean differs from a known value.

The test returns a statistic and a p-value to help decide if the claim holds.

Examples

Test if the average of sample is different from 7.

SciPy

from scipy import stats

sample = [5, 6, 7, 8, 9]
popmean = 7
stat, pvalue = stats.ttest_1samp(sample, popmean)
print(stat, pvalue)

Check if sample mean is different from 10.

SciPy

from scipy import stats

sample = [10, 12, 11, 13, 14]
popmean = 10
stat, pvalue = stats.ttest_1samp(sample, popmean)
print(stat, pvalue)

Sample Program

This code tests if the average test score is really 85 or different. It prints the test result and conclusion.

SciPy

from scipy import stats

# Sample data: test scores after tutoring
scores = [82, 85, 88, 80, 87, 84, 89, 81, 86, 88]

# Claim: average score is 85
claimed_mean = 85

# Perform one-sample t-test
statistic, p_value = stats.ttest_1samp(scores, claimed_mean)

print(f"Test statistic: {statistic:.3f}")
print(f"P-value: {p_value:.3f}")

# Decide if claim is valid at 5% significance
if p_value < 0.05:
    print("Reject the claim: data suggests average is not 85.")
else:
    print("Cannot reject the claim: data supports average is 85.")

Important Notes

A small p-value (usually less than 0.05) means the claim is unlikely true.

Hypothesis testing does not prove a claim, it only shows if data supports or rejects it.

Always check assumptions like data being roughly normal for t-tests.

Summary

Hypothesis testing helps check if data supports a claim or not.

It uses a test statistic and p-value to make decisions.

Small p-value means claim is probably false; large p-value means claim could be true.