The data set in Problems 1.13 and 14.42, shown in the table below for ease of reference, is the time (in months) from receipt to publication of 85 papers published in the January 2004 issue of a leading chemical engineering research journal.
|
19.2
|
15.1
|
9.6
|
4.2
|
5.4
|
|
9.0
|
5.3
|
12.9
|
4.2
|
15.2
|
|
17.2
|
12.0
|
17.3
|
7.8
|
8.0
|
|
8.2
|
3.0
|
6.0
|
9.5
|
11.7
|
|
4.5
|
18.5
|
24.3
|
3.9
|
17.2
|
|
13.5
|
5.8
|
21.3
|
8.7
|
4.0
|
|
20.7
|
6.8
|
19.3
|
5.9
|
3.8
|
|
7.9
|
14.5
|
2.5
|
5.3
|
7.4
|
|
19.5
|
3.3
|
9.1
|
1.8
|
5.3
|
|
8.8
|
11.1
|
8.1
|
10.1
|
10.6
|
|
18.7
|
16.4
|
9.8
|
10.0
|
15.2
|
|
7.4
|
7.3
|
15.4
|
18.7
|
11.5
|
|
9.7
|
7.4
|
15.7
|
5.6
|
5.9
|
|
13.7
|
7.3
|
8.2
|
3.3
|
20.1
|
|
8.1
|
5.2
|
8.8
|
7.3
|
12.2
|
|
8.4
|
10.2
|
7.2
|
11.3
|
12.0
|
|
10.8
|
3.1
|
12.8
|
2.9
|
8.8
|
(i) Using an appropriate probability model for the population from which the data is a random sample, obtain a precise 95% con?dence interval for the mean of this population; use this interval estimate to test the hypothesis by the Editor-in-Chief that the mean time-to-publication is 9 months, against the alternative that it is higher.
(ii) Considering n = 85 as a large enough sample size for a normal approximation for the distribution of the sample mean, repeat (i) carrying out an appropriate one-sample test. Compare your result with that in (i). How good is the normal approximation?
(iii) Use the normal approximation to test the hypothesis that the mean time to publication is actually 10 months, versus the alternative that it is not. Interpret your result vis a' vis the result in (ii).