Hypothesis test for the difference of population means: Paired comparisons

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 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 Table 1.

Worker Process 1 Process 2 Difference

1 79 61 18

2 64 60 4

3 68 50 18

4 77 71 6

5 48 25 23

6 62 42 20

7 87 84 3

8 74 65 9

Based on these data, can the company conclude, at the 0.10 level of significance, that the mean assembly times for the two processes differ? Answer this question by performing a hypothesis test. Perform a two-tailed test and answer the questions below.