Question

The federal government would like to test the hypothesis that the standard deviation for the age of men filing for Social Security is higher than the standard deviation for the age of women. The following table summarizes sample statistics from each population.

	Women	Men
Sample standard deviation	2.6 years	3.3 years
Sample size	24	20

Using

alpha?equals=?0.10,

what is the critical value for this hypothesis? test?

A.

Since the test statistic is less than the? critical? value, we reject the null hypothesis and cannot conclude that the standard deviation for the age of men filing is higher than the standard deviation for the age of womens.

B.

Since the test statistic is less than the? critical? value, we fail to reject the null hypothesis and cannot conclude that the standard deviation for the age of men filing is higher than the standard deviation for the age of womens.

C.

Since the test statistic is more than the? critical? value, we reject the null hypothesis and cannot conclude that the standard deviation for the age of men filing is higher than the standard deviation for the age of womens.

D.

Since the test statistic is more than the? critical? value, we fail to reject the null hypothesis and cannot conclude that the standard deviation for the age of men filing is higher than the standard deviation for the age of womens.

Answer 1

Null Hypothesis

Alternative Hypothesis

Since , We consider in the numerator and in denominator

Therefore, Degrees of Freedom = (n1-1), (n2-1) = (19,23)

The critical value of F for (19,23) df , at 10% significance level is 1.7525

Under H0, the test statistic is

Conclusion :

B. Since the test statistic is less than the? critical? value, we fail to reject the null hypothesis and cannot conclude that the standard deviation for the age of men filing is higher than the standard deviation for the age of womens.