Question

Reserve Problems Chapter 10 Section 3 Problem 2

The manufacturer of bicycles is interested in testing two different tires for bicycle wheels. The tire that is the most wear-resistant would be preferable. The manufacturer obtains 10 samples of each tire types and tests them. The data from the following table show how many kilometers the bicycle will pass before the tire bursts.

Unit 1	954	1000	1099	1090	987	1005	1009	1065	1085	998
Unit 2	1003	1054	900	997	1008	1018	978	1091	1072	1025

Use the Wilcoxon rank-sum test to test  H0: μ1=μ2 against the alternative H1:μ1≠μ2. Use α=0.01.

The parameters of interest are the means of the effectiveness indicator for the two types of promotion.

H0:μ1=μ2

 H1: μ1≠μ2

Because α=0.01 and n1=n2= Enter your answer; Because alpha=0.01 and n1=n2=, the critical value of the rank sums is wα=w0.01= Enter your answer; the critical value of the rank sums is w_alpha=w_0.01=. If either w1 or w2 is Choose your answer; If either w1 or w2 is _ w_0.01

greater than or equal toequal toless than or equal togreater thanless than

w0.01= Enter your answer; w_0.01= , we will reject  H0: μ1=μ2.

The data are arranged in the ascending order and ranked as follows:
(Enter the missing values.)

Unit	Kilometers	Rank
2	900	1
1	954	2
Enter your answer; Unit for Rank = 3	Enter your answer; Kilometers for Rank = 3	3
Enter your answer; Unit for Rank = 4	Enter your answer; Kilometers for Rank = 4	4
2	997	5
1	998	6
Enter your answer; Unit for Rank = 7	Enter your answer; Kilometers for Rank = 7	7
Enter your answer; Unit for Rank = 8	Enter your answer; Kilometers for Rank = 8	8
1	1005	9
2	1008	10
1	1009	11
2	1018	12
2	1025	13
2	1054	14
1	1065	15
2	1072	16
1	1085	17
1	1090	18
2	1091	19
1	1099	20

The test statistics are

w1=Enter your answer; w1

and

w2=Enter your answer; w2

Conclusion: Because neither w1 or w2 is Choose your answer; Because neither w1 or w2 is _ w_0.01

greater than or equal toequal toless thanless than or equal togreater than

w0.01, we Choose your answer; we _ reject the null hypothesis that both types of tires exhibit the same mean distance passed before the tires burst

cancannot

reject the null hypothesis that both types of tires exhibit the same mean distance passed before the tires burst.

Answer 1