Discussion:
Q: A personal computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Process 1 is an updated process hoped to bring a decrease in assembly time, while Process 2 is the standard process used for several years. Assembly times can vary considerably from worker to worker, and the company decides to eliminate this effect by selecting a random sample of 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
Worker Process 1 Process 2 Difference
(Process 1 - Process 2)
1 75 61 14
2 77 90 -13
3 84 57 27
4 43 54 -11
5 62 64 -2
6 33 34 -1
7 55 34 21
8 76 73 3
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 U 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. ( note= U is the Greek letter "MU")
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.
The null hypothesis
The alternative hypothesis
The type of test statistic
The value of test statistic
The two critical values at the 0.10 significance level
At the 0.10 significance level, can the company conclude that the mean assembly times for the two processes differ? ( yes or no)