The data in the following table was analyzed to test a hypothesis about the mean time-to-publication for papers sent to a particular leading chemical engineering research journal. The data shows the time (in months) from receipt to publication of 85 papers published in the January 2004 issue of this journal.
(i) On phenomenological grounds, and from past experience, a gamma distribution has been postulated for the population from which the data was sampled. The population parameters are unavailable. Carry out an A-D test to validate this probability model postulate.
(ii) In recognition of the fact that the underlying distribution is obviously skewed, the Editor-in-Chief has modi?ed his hypothesis about the characteristic time-to- publication, and now proposes that the mediantime-to-publication is 8 months. Carry out an appropriate test to assess the validity of this statement against the alternative that the median time-to-publication is not 8 months. Interpret your re- sults.
(iii) Repeat the test in (ii), this time against the alternative that the median time- to-publication is longer than 8 months. Reconcile this result with the one in (ii).
|
19.2
|
15.1
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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
|