Persons submitting computing jobs to a computer center usually are required to estimate the amount of computer time required to complete the job. This time is measured in CPUs, the amount of time that a job will occupy a portion of the computer's central processing unit's memory. A computer center decided to perform a comparison of the estimated versus actual CPU times for a particular customer. The corresponding times were available for 11 jobs. The sample data are given in the accompanying table.
|
CPU Time
|
Job Number
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(minutes)
|
I
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
|
Estimated
|
.50
|
1.40
|
.95
|
.45
|
.75
|
1.20
|
1.60
|
2.6
|
1.30
|
.85
|
.60
|
|
Actual
|
.46
|
132
|
.99
|
.53
|
.71
|
1.31
|
149
|
2.9
|
1.41
|
.83
|
.74
|
a Why would you expect that the observations within each of these pairs of data to be correlated?
b Do the data provide sufficient evidence to indicate that, on the average, the customer tends to underestimate the CPU time required for computing jobs? Test using α=.10.
c Find the observed significance level for the test and interpret its value.
d Find a 90% confidence interval for the difference in mean estimated CPU time versus mean actual CPU time.