Question

At a college, 61 female students were randomly selected and it was found that their monthly income had a standard deviation of $230.85. For 121 male students, the standard deviation was $320.53. Test the claim that variance of monthly incomes is higher for male students than it is foi female students. Use a = 0.01.

Answer 1

= The provided sample variances are sỉ = 53291.7225 and sź = 102739.4809 and the sample sizes are given by ni = 61 and n2 = 121. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: o =02 Ha:< o This corresponds to a left-tailed test, for which a F-test for two population variances needs to be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.01, and the the rejection region for this left-tailed test is R={F:F< F1 = 0.579}.

(3) Test Statistics The F-statistic is computed as follows: F = 53291.7225 102739.4809 = 0.519 (4) Decision about the null hypothesis Since from the sample information we get that F = 0.519 < Fi = 0.579, it is then concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population variance oí is less than the population variance oż, at the a = 0.01 significance level.

Final conclusion: We cannot support the claim that the variance of monthly income is higher for male students than it is for female students