Question

You have been assigned to test the hypothesis that the variability for the number of hours per week that an American works is equal to the variability for the number of hours per week that a Swede works. The following data summarizes the sample statistics for the number of hours worked per week for workers in each country.

	American	Swede
Sample standard deviation	5.5 hours	6.2 hours
Sample size	17	13

Using

alpha?equals=?0.10,

what is the conclusion for this hypothesis? test?

A.

Since the test statistic is less than the critical? value, we fail to reject the null hypothesis and conclude that the variability for the number of hours per week that an American works is equal to the variability for the number of hours per week that a Swede works

B.

Since the test statistic is more than the critical? value, we fail to reject the null hypothesis and conclude that the variability for the number of hours per week that an American works is not equal to the variability for the number of hours per week that a Swede works

C.

Since the test statistic is more than the critical? value, we reject the null hypothesis and can conclude that the variability for the number of hours per week that an American works is not equal to the variability for the number of hours per week that a Swede works

D.

Since the test statistic is less than the critical? value, we fail to reject the null hypothesis and cannot conclude that the variability for the number of hours per week that an American works is not equal to the variability for the number of hours per week that a Swede works

Answer 1

This is the case of a two-tailed F test.

The hypotheses are:

H0: =

Ha:

Here the subscript 1 is for American and 2 os for Swedish.

Calculating F-statistic:

F = / = (5.5^2)/(6.2^2) = 0.787

Next we calculate degrees of freedom:

df1 = 17-1 = 16

df2 = 13-1 = 12

Significance level, a = 0.10

Since this is a two tailed test. we divide a by 2, so the significance level is 0.05

So, Critical F-value, F_c = 2.598

Since F < F_c, so we cannot reject the null hypothesis.

Since the test statistic is less than the critical? value, we fail to reject the null hypothesis and conclude that the variability for the number of hours per week that an American works is equal to the variability for the number of hours per week that a Swede works