A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics exam has a standard deviation that is less than 5.0 minutes. A random sample of 15 students was selected and the sample standard deviation for the time needed to complete the exam was found to be 4.0 minutes. Using α=0.05, determine the critical value for this hypothesis test. Round to three decimal places.

The critical value for this hypothesis test is 6.571.

Step-by-step explanation:

In this case the professor wants to determine whether the average number of minutes that a student needs to complete a statistics exam has a standard deviation that is less than 5.0 minutes.

Then the variance will be,

The hypothesis to determine whether the population variance is less than 25.0 minutes or not, is:

H₀: The population variance is not less than 25.0 minutes, i.e. σ² = 25.

Hₐ: The population variance is less than 25.0 minutes, i.e. σ² < 25.

The test statistics is:

The decision rule is:

If the calculated value of the test statistic is less than the critical value, then the null hypothesis will be rejected.

Compute the critical value as follows:

*Use a chi-square table.

Thus, the critical value for this hypothesis test is 6.571.