Question

4. A random sample of 12 second-year university students enrolled in a business statistics course was drawn. At the course's completion, each student was asked how many hours he or she spent doing homework in statistics. The data are listed below. It is known that the population standard deviation is o= 8.0. The instructor has recommended that students devote 3 hours per week for the duration of the 12-week semester, for a total of 36 hours. At 10% significance level (a), determine whether there is evidence that the average student spent less than the recommended amount of time. Be sure to also compute the p-value of the test. How does it inform your decision? 31 40 26 30 36 38 29 40 38 30 35 38

Answer 1

Ho: mean=36 hours

Ha : mean < 36

Rejection region is to the left of z = - 1.28 ( as Z_0.10 = 1.28)

Mean = (31 +40+ 26 +30+ 36 +38+ 29 +40+ 38 +30+ 35+ 38)/12 = 34.25

Test statistics :

Z = (34.25-36)/(8/(12)^0.5) = - 0.7578

P -value = 0.22429

Since test Z score does not fall in the rejection region, we fail to reject the null hypothesis.

Or

As P- value > 0.10, we reject the null hypotheis

We fail to reject the null hypothesis. There is not sufficient evidence to show that students study for less than 36 hours.