Question

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 10 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: 1,2,3,4,5,6,7,8,9,10

Process 1: 61,71,68,58, 81,67,38,31,49,80

Process 2: 54,68,61,55,59,74,21,41,47,78

Difference
(Process 1 - Process 2): 7,3,7,3,22,-7, 17, -10,2,2

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 μd (which is μwith 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 fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

Null Hypothesis: ?

Alternative Hypothesis: ?

Type of test statistic: ? (z, t, chi square, F)

The value of the test statistic: ? (round to 3 decimal places)

The two critical values at the .10 level of significance: ? and ? (round to 3 decimal places)

At the .1 level, can the company conclude that the mean assembly times for the two processes differ? (yes or no)

Answer 1