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 parameters have not been speci?ed.
(ii) Using only the top half of each data set, repeat (i). For this particular example, what effect, if any, does sample size have on the probability plots approach to probability model validation?