Appendix A.34

Standard Deviation Hypothesis Test

Perform hypothesis tests for a single population standard deviation using chi-square.

Hypothesis Test Calculator for Population Standard Deviation (χ²-test)

Test claims about population variability using the chi-square distribution

Important: This test requires the population to be normally distributed. It is NOT robust to departures from normality.

Enter:

Hypotheses

Null:
Alternative:
df:
24

Calculations

Sample Variance
Sample Std Dev
Hypothesized Variance
Test Statistic

χ² Distribution (df = 24)

12.4139.35χ² = 34.56RejectRejectFail to Reject

Classical Approach

Critical Region: χ² < 12.414 or χ² > 39.351
χ₀² = 34.5600 is NOT in rejection region

P-Value Approach

P-value = 0.1504
P-value ≥ α = 0.05

Fail to Reject H₀

At the α = 0.05 significance level, there is insufficient evidence to conclude that the population standard deviation differs from 2.