Question

Try yourself 9.2 The 40-hour work week did not become a U.S. standard until 1940. Today, many white-collar employees work more than 40 hours per week because management demands longer hours or offers large monetary incentives. A random sample of white-collar employees was obtained, and the number of hours each worked during the last week are given in the following table. 44.7 42.0 45.8 43.0 42.8 50.9 47.0 41.9 49.3 45.6 45.7 39.4 39.0 44.4 Is there any evidence the true mean number of hours worked by white-collar employees is greater than 40? Use a 5 0.01. What assumption(s) did you make in order to complete this hypothesis test? (You can do this in two ways 1. by finding the rejection region 2. by reporting a p-value.)

Answer 1

Count, N: 14 Sum, Ex: 621.5 Mean, 44.392857142857 Variance, s2: 11.453021978022 Steps N 1 S = (xi – T), N-1 i=1 S2= 11 (xi - x)2 N-1 (44.7 - 44.392857142857)2 + .... + (44.4 - 44.392857142857)2 14-1 148.88928571429 13 = 11.453021978022 S= V11.453021978022 = 3.3842313718217

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: u s 40 Ha: u > 40 This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.01, and the critical value for a right-tailed test is te = 2.65. The rejection region for this right-tailed test is R=t:t> 2.65 (3) Test Statistics The t-statistic is computed as follows: x - до t= 44.3928 - 40 3.3842/14 = 4.857 8/n

(4) Decision about the null hypothesis Since it is observed that t = 4.857 > te = 2.65, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p= 0.0002, and since p= 0.0002 <0.01, 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 the population mean u is greater than 40, at the 0.01 significance level.