Statistics > Hypothesis Tests > 1-Population Variance

This utility performs calculations for testing claims about a population variance (or standard deviation). The population is assumed to have a normal distribution. The null hypothesis of a claim about a population variance σ2 is &sigma = &sigma02. The alternative hypothesis can be one of the following: σ < σ0, σ > σ0, or σ ≠ σ0.

The test statistic is computed using the following formula:

where s is the sample standard deviation, σ is the hypothesized population standard deviation, and n is the sample size.

To use the utility, follow these steps:

Sample Outputs

The null hypothesis and the alternative hypothesis are displayed. The results, along with the input parameters, are displayed in a table.
[N = sample size; Sample Stdev s = sample standard deviation calculated from the individual samples or provided directly by the user; Sample Var s2 = sample variance; Significance Level = 1 - confidence level; Critical Value = critical value corresponding to the significance level; Test Statistic = test statistic corresponding to the hypothesized variance; p-Value = p-Value corresponding to the test statistic]



Hypothesis Test - One population variance: confidence level = 0.95
Input: Summary data
Null hypothesis: σ2 = 1.44
Alternative hypothesis: σ2 ≠ 1.44

N Sample Stdev s Sample Var s2 Significance Level Critical Value Test Statistic p-Value
100 1.500 2.250 0.05 73.361, 128.422 154.688 0.0006