The sample variance is 2.976 , which means it's lesser than 6.25. We calculate this using the standard method.
Given:
Sample data is 0.05
The sample size is 20.
And ,
The hypotheses are:
H0: sigma^2 = 6.25 (>=)
Ha: sigma^2 < 6.25
The critical value is 10.117. If the test statistic is less than this value, we'll reject the null hypothesis. We Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the p-value is low, the null must go.
The test statistic is:
2.976 * 19 / 6.25 = 9.047.
So we reject the null hypothesis. The variance is not 6.25, which means it is lesser then 6.25
To learn more about the sample variance.
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