Question

In a certain problem, the randomization test produces an exact two-sided p-value of 0.053, while the t -distribution approximation produces 0.047. One might say that since the p-values are on opposite sides of 0.05, they lead to quite different conclusions and, therefore, the approximation is not adequate. Comment on this statement.

Answer 1

Using randomization test , P value is 0.053 and t distribution approximation p value is 0.047. For both method conclusions are different.

The Randomization test is adequate and t distribution approximation is not adequte because randomization test gives exact value of p . And t distribution approximation gives approximate p value.

Randomization test conducted using chance method but t distribution approximation. Test using random sample. Hence t distribution approximation test not adequte