Question

1. The manufacturer of a hot tub is interested in testing two different heating elements for its product. The element that produces the maximum heat gain after 15 minutes would be preferable. The manufacturer obtains 10 samples of each heating element and tests each one. The heat gain after 15 minutes (in °F) follows.

Unit 1: 25, 27, 29, 31, 30, 26, 24, 32, 33, 38

Unit 2: 31, 33, 32, 35, 34, 29, 38, 35, 37, 30

1. Using a non-parametric test at 5% alpha level, is there any reason to suspect that one unit is superior to the other?

H0 : μ1=μ2

H1 : μ1≠μ2

Unit #	Heat	Rank
1	24	1
1	25	2
1	26	3
1	27	4
1	29	5.5
2	29	5.5
1	30	7.5
2	30	7.5
1	31	9.5
2	31	9.5
1	32	11.5
2	32	11.5
1	33	13.5
2	33	13.5
2	34	15
2	35	16.5
2	35	16.5
2	37	18
1	38	19.5
2	38	19.5

Sum of ranks
Unit 1

W1 = 1 + 2 + 3 + 4 + 5.5 + 7.5 + 9.5 + 11.5 + 13.5 + 19.5 = 77

Unit 2

(n1+n2)(n1+n2+1)2 – w1

= (10 +10)(10+10+1)2 – w1

= 133

Using Critical Values table

w0.05=78

Since 77 < 78

We Reject the Null Hypothesis

b) Solve part (a) by Minitab and report the results. ( I do not have Minitab Please help)

Answer 1

pvalue is 0.006 < 0.05 hence reject null hypothesis