Question

At the .10 significance level can we conclude that there is a difference in the variation of sick days of men vs. women? 21 men took on average 10 sick days with a standard deviation of 4 days. 21 women took on average 12 sick days with a standard deviation of 3 days. (Use F value of 2.16)

Do we reject or do not reject?

is there a difference in the two populations?

Answer 1

The provided sample means are shown below: X1 = 10 X2 = 12 Also, the provided sample standard deviations are: Si = 4 S2 = 3 and the sample sizes are ni = 21 and n2 = 21. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: p1 = M2 Ha: Mi 7 H2

This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.10, and the degrees of freedom are df = 37.092. In fact, the degrees of freedom are computed as follows, assuming that the population variances are unequal: Hence, it is found that the critical value for this two-tailed test is te = 1.687, for a = 0.10 and df = 37.092. The rejection region for this two-tailed test is R= {t: \t| > 1.687}. (3) Test Statistics Since it is assumed that the population variances are unequal, the t-statistic is computed as follows:

X1 - X2 t= + n2 10 - 12 -1.833 42 + 32 21 (4) Decision about the null hypothesis Since it is observed that t = 1.833 > to = 1.687, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p = 0.0748, and since p = 0.0748 < 0.10, it is 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 population mean ui is different than 42, at the 0.10 significance level.

Final conclusion: Yes; There is difference in the two populations