Question

A personal computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Asse 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 first. For each worker and each process, the assembly time (in minutes) is recorded, as shown in Table 1. mbly times can workers are chosen at random to use Process 1 first, and the rest use Process 2 Difference Worker Process 1 Process 2 (Process 1 - Process 2) 32 52 46 72 61 36 57 19 17 39 18 69 85 90 70 30 67 10 Table 1 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 regarding Ha (which is u with a letter "d" subscript) assembly times for the two processes. Assume that this population of differences (Process 1 minus Process 2) is normally Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at distributed. least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

Answer 1

Solution: The data provided in the question statement can be tabulated as below. Calculating a few additional columns Worker Process 1 Process 2 Difference d= X1-X2 54 69 85 90 70 30 67 32 52 46 72 61 36 57 19 (d - d)2 43.891 2.641 558.141 6.891 40.641 456.891 28.891 1.891 17 39 18 4 6 -6 10 14 yd 123 8 d- d2- 1139.875 d-d /n 123/8 15.375 Sd = D (d-d) 리(n-1)-v/1139.875/(8-1)-12.761 The null hypothesis The alternative hypothesis: The type of test statistic: Value of test Statistic: H1: Id 0 t (15.375-0)/ (12.761//8) 3.408

Degrees of freedom df n-1 8-1 7 Critical Values: Significance level, α-0.10 The test is a two tailed test. a/2 0.10/2 0.05 From t-distribution table; the critical value of 't', having area in the upper tail equal to 0.05 and for (df 7), is given by: to ritical-1.895 Since the test is a two tailed test, the critical values are =-1.895, 1.895 Conclusion Based on the critical values above, the rejection region is: (-00,-1.895) U (1.895,00) Since the value of test statistic (t 3.408) falls in the rejection region above, we reject the null hypothesis. Therefore, the company can conclude that the mean assembly times for the two processes differ.