The data in the table below are from two populations that may or may not be the same.
|
XU
0.65
|
YU
1.01
|
|
2.01
|
1.75
|
|
1.80
|
1.27
|
|
1.13
|
2.48
|
|
1.74
|
2.91
|
|
1.36
|
2.38
|
|
1.55
|
2.79
|
|
1.05
|
1.94
|
|
1.55
|
|
|
1.63
|
|
(i) Carry out a two-sample t test to compare the population means. What assumptions are required for this to be a valid test? At the α = 0.05 signi?cance level, what does this result imply about the null hypothesis?
(ii) Carry out a MWW test to determine if the two populations have the same medians or not. At the α = 0.05 signi?cance level, what does this result imply about the null hypothesis?
(iii) It turns out that the data were generated from two distinct uniform distributions, where the Y distribution is slightly di?erent. Which test, the parametric or the nonparametric, is more effective in this case? Offer some reasons for the observed performance of one test versus the other.
(iv) In light of what was speci?ed about the two populations in (iii), and the p-values associated with each test, comment on the use of α = 0.05 as an absolute arbiter of signi?cance.