Question

a sample of 60 items from population 1 has a sample variance of 12 while a sample of 50 items from population 2 has a sample variance of 15. if we want to test whether the variances of the two populations are equal, the test statistic will have a value of

Answer 1

The test statistic to test whether the variances of the two populations are equal using an F-test is 1.25. The F statistic is calculated as the ratio of the larger sample variance to the smaller sample variance.

Step-by-step explanation:

When testing whether the variances of two populations are equal, we can use the F-test for equality of two variances which is under the assumption that both populations follow a normal distribution.

The F statistic is calculated by dividing the larger sample variance by the smaller sample variance. In this case, the sample variance of population 2 (15) is divided by the sample variance of population 1 (12), resulting in an F statistic of 1.25.

This ratio is then compared to a critical value from the F distribution table, with degrees of freedom df1 = n1 - 1 = 59 for the numerator and df2 = n2 - 1 = 49 for the denominator, to determine whether the observed variances are significantly different at a given level of significance (alpha).