Question

A personal computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Asserbly 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. Difference Worker Process Process 2 (Process 1 - Process 2) 1 82 66 30 16 4 34 2 3 54 15 4 39 12 79 51 80 71 8 5 6 72 35 36 6 36 7 B 42 68 54 Tablet Based on these data, can the company condude, 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 H. (which is with a letter "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 fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table

Answer 1

Sof: Given dala 16, 4, 15, 12 8, 36, 6, 14 zo 111 a = 13.875 Erd² (16-13.875² + +(14-13.875) std de 8-) 9.949 Null hypothesis : Ho: Mdao Alternative hypothesis H, Mapo . Type of test stastistic (paired) t-test و لر -م Test statistic t = 13.875-0 3.944 slin 9.999158 tal = 3.944 a-0.05 df = 7 Critical values tenit to, df et 2.3646 0.0025 7 + 2.841 +2.841 1 2,841 teal tenit Hence we reject Ho ge 0.05 Conclusim. Reject to -2.841 2.84)