A personal computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Process 1 is the standard process used for several years, and Process 2 is an updated process hoped to bring a decrease in assembly time. Assembly times can vary considerably from worker to worker, and the company decides to eliminate this effect by selecting a random sample of 8 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 Process 1 86 53 43 64 34 85 46 80 Process 2 82 32 33 37 11 87 44 47 Difference (Process 1 - Process 2) 4 21 10 27 23 −2 2 33 Based on these data, can the company conclude, at the 0.10 level of significance, that the mean assembly time for Process 1 exceeds that of Process 2? Answer this question by performing a hypothesis test regarding μd (which is μ with a letter "d" subscript), the population mean difference in assembly times for the two processes. Assume that this population of differences (Process 1 minus Process 2) is normally distributed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. a. State the null hypothesis H0 and the alternative hyposthesis H1. b. Find the value of the test statistic. Round to three or more decimal places. c. Find the critical value at the 0.10 level of significance. Round to three or more decimal places. d. At the 0.10 level, can the company conclude that the mean assembly time for Process 1 exceeds that of Process 2?
A personal computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Process 1 is the standard process used for several years, and Process 2 is an updated process hoped to bring a decrease in assembly time. Assembly times can vary considerably from worker to worker, and the company decides to eliminate this effect by selecting a random sample of 8 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
|
|---|---|---|---|---|---|---|---|---|
| Process 1 |
86
|
53
|
43
|
64
|
34
|
85
|
46
|
80
|
| Process 2 |
82
|
32
|
33
|
37
|
11
|
87
|
44
|
47
|
| Difference (Process 1 - Process 2) |
4
|
21
|
10
|
27
|
23
|
−2
|
2
|
33
|
Based on these data, can the company conclude, at the 0.10 level of significance, that the
a. State the null hypothesis H0 and the alternative hyposthesis H1.
b. Find the value of the test statistic. Round to three or more decimal places.
c. Find the critical value at the 0.10 level of significance. Round to three or more decimal places.
d. At the 0.10 level, can the company conclude that the mean assembly time for Process 1 exceeds that of Process 2?
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