Question

17-52.

Most students who attend Upper Mountain Community College buy their textbooks online from one of two different booksellers because the college does not have a bookstore. The following data represent sample amounts that students spend on books per term:

Company 1 ($)	Company 2 ($)
246	300
211	305
235	308
270	325
411	340
310	295
450	320
502	330
311	240
200	360

a. Do these data indicate a difference in mean textbook prices for the two companies? Apply the Mann Whitney U-test with a significance level of 0.10.

b. Apply the t-test to determine whether the data indicate a difference between the mean amounts spent on books at the two companies. Use a significance level of 0.10. Indicate what assumptions must be made to apply the t-test.

Answer 1

a)

U - Test:
H0: There is no sigificance difference between the company 1 and company 2
H1: There is significance difference between the company 1 and company 2

Original Data		Ranks
Company 1	Company 2	Company 1	Company 2
246	300	5	8
211	305	2	9
235	308	3	10
270	325	6	14
411	340	18	16
310	295	11	7
450	320	19	13
502	330	20	15
311	240	12	4
200	360	1	17
	Total:	97	113

Here P-value > alpha 0.10 so we accept H0

Thus we conclude that  There is no sigificance difference between the company 1 and company 2

b) t - test:

H0: There is no sigificance difference between the company 1 and company 2
H1: There is significance difference between the company 1 and company 2

Critical t: ±1.800988
P-Value: 0.9485

Here t value is lies critical values of t and P-value > alph a0.05 so we accept H0

thus we conclude that there is no sigificance difference between the company 1 and company 2