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 Process 1 Process 2 Difference (Process 1 - Process 2) 1 32 20 12 2 82 46 36 3 42 24 18 4 65 57 8 5 45 49 -4 6 32 14 18 7 63 60 3 8 48 17 31 9 53 56 -3 10 85 76 9

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 μd (which is μ 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 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.)

The null hypothesis: H0 : The alternative hypothesis: H1 : The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic: (Round to at least three decimal places.) The two critical values at the 0.10 level of significance: (Round to at least three decimal places.) and At the 0.10 level, can the company conclude that the mean assembly times for the two processes differ? Yes No

Answer 1

null Hypothesis:μd		=	0
alternate Hypothesis: μd		≠	0

The type of test statistic: t

3)

total	=	Σd=128
mean dbar=	d̅                           =	12.80
degree of freedom =n-1                            =		9.000
Std deviaiton SD=√(Σd2-(Σd)2/n)/(n-1) =		13.290
std error=Se=SD/√n=		4.203
value of    test statistic            =	(d̅-μd)/Se         =	3.046

The two critical values at the 0.1 level =-1.833 and 1.833

4)

At the 0.10 level, can the company conclude that the mean assembly times for the two processes differ "Yes degree of freedom =9