The following data shows annual income,in thousands of dollars,categorized according to the two factors of gender and level of education.Assume that incomes are not affected by an interaction between gender and level of education,and test the null hypothesis that gender has no effect on income and that level of education has no effect on income.Use a 0.05 significance level.

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: = ,where γ represents gender. :gender has an effect on income.The test statistic is F = 0.16954,and the corresponding P-value is 0.6849.Because the P-value is greater than 0.05,we fail to reject the null hypothesis that gender has no effect on income. : = = ,where τ represents level of education. :Education level has an effect on income.The test statistic is F = 44.96689,and the corresponding P-value is 0.0000000397.Because the P-value is less than 0.05,we reject the null hypothesis that education level has no effect on income.It appears that education level does have an effect on income.

:

=

,where γ represents gender.

:gender has an effect on income.The test statistic is F = 0.16954,and the corresponding P-value is 0.6849.Because the P-value is greater than 0.05,we fail to reject the null hypothesis that gender has no effect on income.

:

=

,where τ represents level of education.

:Education level has an effect on income.The test statistic is F = 44.96689,and the corresponding P-value is 0.0000000397.Because the P-value is less than 0.05,we reject the null hypothesis that education level has no effect on income.It appears that education level does have an effect on income.

The Following Data Shows Annual Income,in Thousands of Dollars,categorized According