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 of10 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.

Based on these data, can the company conclude, at the 0.05 level of significance, that the mean assembly times for the two processes differ? Answer this question by performing a hypothesis test regarding ?d (which is ? 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 two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. (If necessary, consult a list of formulas.)

Worker 2 3 4 5 6 7 8 9 10 Process 1 89 77 66 66 87 55 69 55 73 36 Process 2 70 58 81 58 101 58 49 37 59 32 Difference (Process 1 - 19 19 -15 8 -14 -3 20 18 14 4 Process 2) (a) State the null hypothesis / and the alternative hypothesis H, P S P (6) Determine the type of test statistic to use. Type of test statistic: (Choose one) 0-0 OSO 020 c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.) X [and (e) At the 0.05 level, can the company hat the mean assembly times for the two processes Yes No