A computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Assembly times ca

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A 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
10
workers at random 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
the table below.
Worker
1
2
3
4
5
6
7
8
9
10
Process 1
31
59
48
82
42
84
33
30
71
30
Process 2
44
58
54
56
34
88
29
20
52
26
Difference
(Process 1 - Process 2)
−13
1
−6
26
8
−4
4
10
19
4
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Based on these data, can the company conclude, 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
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 complete the parts below. Carry
your intermediate computations to three or more decimal places and
round your answers as specified. (If necessary, consult a list
of formulas.)
(a)
State the null hypothesis
H0
and the alternative hypothesis
H1
.
H0:
H1:
(b)
Determine the type of test statistic to use.
Type of test statistic: ▼(Choose one)
(c)
Find the value of the test statistic. (Round to three or more
decimal places.)
(d)
Find the two critical values at the
0.05
level of significance. (Round to three or more decimal
places.)
and
(e)
At the
0.05
level, can the company conclude that the mean assembly
times for the two processes differ?
Yes
No