Question

Suppose Sony would like to test the hypothesis that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users. The following table summarizes sample statistics from each population.

	Playstation	Xbox
Sample standard deviation	6.5years	1.9 years
Sample size	25	28

Using

alpha?equals=?0.05,

what is the conclusion for this hypothesis? test?

A.

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 PlayStation users is higher than the standard deviation for the age of Xbox users.

B.

Since the test statistic is less than the critical? value, we fail to reject the null hypothesis and conclude that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users.

C.

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 PlayStation users is higher than the standard deviation for the age of Xbox users.

D.

Since the test statistic is more than the critical? value, we fail to reject the null hypothesis and conclude that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users.

Answer 1

Here we need to do F test. So hypotheses are :

Test is right tailed.

Here we have

Test statistics wil be

Degree of freedom of numerator: df1=n1 -1 = 24

Degree of freedom of denominator: df2=n2 -1 = 27

The p-value is: 0.0000

The critical value is; 1.930

Since F is greater than critical value so we reject the null hypothesis.

Since the test statistic is more than the critical? value, we reject the null hypothesis and can conclude that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users.