Question

if s2¹ and s2² represent the variances of independent dent random samples of size n1 is 8 and n2 is 12, taken from normal populations with equal variances, p (s2¹ /s2² < 4.89). 7

Answer 1

The F-test is used to test the equality of variances between two independent random samples. In this case, we are comparing the variances of two samples with sizes 8 and 12. The null hypothesis is that the variances are equal, and the alternative hypothesis is that the variance of the first sample is smaller than the variance of the second sample.

Step-by-step explanation:

F-test is used to test the equality of variances between two independent random samples. In this case, we have two independent samples with different sizes: n1 = 8 and n2 = 12.

The null hypothesis is that the variances are equal, while the alternative hypothesis is that the variance of the first sample is smaller than the variance of the second sample.

To test this hypothesis, we calculate the F-statistic, which is the ratio of the variances: F = s1^2 / s2^2.

In this case, F = (s2^2) / (s1^2). We compare this F-statistic with the critical value of 4.89 to determine if we reject or fail to reject the null hypothesis.