A survey was given In two statistics classes on the number of hours students slept the night before. One class was a liberal arts class; the other class was a general introductory class. The survey was given following a Sunday night after classes had started. For slmpllcity. let's assume that these classes represent a random sample of sleep hours for college students in liberal arts and non-Iibelal arts majors. The data are as follows. standard Mean Deviation Ubalalar'ts 25' 7.67 I 1.35 I Non-libelalarts 148' 6.81 I 1.?2 I (a) Test the hypothesis that the mean number of hours of sleep for the two populations of students are equal versus the alternative that they are not equal. use the unpooled ttest with o: = 0.05. (Note: The approximate df = 38 for the unpooled test.) 0 Reject the null hypothesis. There is evidence to conclude that the mean number of hours of sleep for the two populations of students are not equal. D Do not reject the null hypothesis. There ls not evidence to conclude that the mean number of hours of sleep for the two populations of students are not equal. Eb} 111s gure below displays a doth-ot ofthe dam. Nonliberoloris I I I I I n I I I I 0' I I i I I a n liberoloris o'cloloI '0 l2 Y Hours ol'sleep (D Briefly explain what is indicated about the necessary conditions for doing a two-sample t-test. The dotplot shows that the liberal arts data is n-Selactm VI and ---Se|eot-- V , and the non-liberal arts data is w and . So the conditions for doing a two-sample t-test satised. {c} Repeat the hypothesis test using the pooled procedure with o' = 0.05. O Reject the null hypothesis. There is eyldence to conclude that the mean number of hours of sleep for the two populations of students are not equal. 0 Do not reject the null hypothesis. 111ere is not evidence to conclude that the mean number of hours of sleep for the two populations of students are not equal. Compare the results to those in part {a}. The p-yalue for the pooled prooedure ls Se|ect v the p-yalue tor the unpooled procedure, and the conclusions for the two tests the same. Discuss which procedure you think is more appropriate in this situation. Because the two sample sizes are very tifferent, the procedure is preferable. However, the procedure is acceptable in this case, since the standard deviations of the samples are about the same and the larger sample has the standard deviation