State the null hypothesis H0 and the alternative hypothesis H1. b. Find the value of the test statistic. Round to three or more decimal places. c. Find the two critical values at the 0.05 level of significance. Round to three or more decimal places. d. At the 0.05 level, can the company conclude that the mean assembly times for the two processes differ?
A personal computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Assembly times can vary considerably from worker to worker, and the company decides to eliminate this effect by selecting a random sample of 12 workers and timing each worker on each assembly process. Half of the workers are chosen at random to use Process 1 first, and the rest use Process 2 first. For each worker and each process, the assembly time (in minutes) is recorded, as shown in the table below.
| Worker |
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Process 1 |
78
|
74
|
57
|
50
|
58
|
59
|
76
|
34
|
89
|
76
|
71
|
88
|
| Process 2 |
50
|
68
|
47
|
52
|
41
|
62
|
59
|
14
|
81
|
65
|
34
|
71
|
| Difference (Process 1 - Process 2) |
28
|
6
|
10
|
−2
|
17
|
−3
|
17
|
20
|
8
|
11
|
37
|
17
|
Based on these data, can the company conclude, at the 0.05 level of significance, that the
a. State the null hypothesis H0 and the alternative hypothesis H1.
b. Find the value of the test statistic. Round to three or more decimal places.
c. Find the two critical values at the 0.05 level of significance. Round to three or more decimal places.
d. At the 0.05 level, can the company conclude that the mean assembly times for the two processes differ?
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