The data in the following table (Exercise 12.12) shows samples of size n = 20 drawn from four different populations postulated to be normal, N , lognormal L, gamma G, and inverse gamma I, respectively.
|
XN
9.3745
|
XL
7.9128
|
XG
10.0896
|
XI
0.084029
|
|
8.8632
|
5.9166
|
15.7336
|
0.174586
|
|
11.4943
|
4.5327
|
15.0422
|
0.130492
|
|
9.5733
|
33.2631
|
5.5482
|
0.115567
|
|
9.1542
|
24.1327
|
18.0393
|
0.187260
|
|
9.0992
|
5.4151
|
17.9543
|
0.100054
|
|
10.2631
|
16.9556
|
12.5549
|
0.101405
|
|
9.8737
|
3.9345
|
9.6640
|
0.100835
|
|
7.8192
|
35.0376
|
14.2975
|
0.097173
|
|
10.4691
|
25.1182
|
4.2599
|
0.141233
|
|
9.6981
|
1.1804
|
19.1084
|
0.060470
|
|
10.5911
|
2.3503
|
7.0735
|
0.127663
|
|
11.6526
|
15.6894
|
7.6392
|
0.074183
|
|
10.4502
|
5.8929
|
14.1899
|
0.086606
|
|
10.0772
|
8.0254
|
13.8996
|
0.084915
|
|
10.2932
|
16.1482
|
9.7680
|
0.242657
|
|
11.7755
|
0.6848
|
8.5779
|
0.052291
|
|
9.3790
|
6.6974
|
7.5486
|
0.116172
|
|
9.9202
|
3.6909
|
10.4043
|
0.084339
|
|
10.9067
|
34.2152
|
14.8254
|
0.205748
|
(i) Validate these postulates using the full data sets. Note that the population pa- rameters have not been speci?ed.
(ii) Using only the top half of each data set, repeat (i). For this particular exam- ple, what effect, if any, does sample size have on the probability plots approach to probability model validation?