Answer to Question #316052 in Statistics and Probability for Seemu

Question

State whether the following statements are true or false and reason for support it

(1) If the level of significance is the same, the area of the rejection region in a two tailed test is less than that in a one tailed test.

(2)Non parametric tests are more powerful than the parametric tests

(3)If T1 and T2 are two estimators of the parameter theta such that varience of T2 =1/n and varience of T2=n then T1 is more efficient than T2

Answer 1

1. False. In both one tail and two tail test the level of significance is the same thus the rejection areas are equal .For instance if the level of significance in both test is 0.05 the rejection area for a one tailed test is 0.05 and the rejection area for a two tailed test is 0.025 on one side and 0.025 on the other side.
2. False .Parametric test are more powerful than non parametric .Non parametric test such as  Wilcoxon Signed Rank test and Mann-Whitney test are use in cases where parametric test are not appropriate .Mainly non parametric use a kind of ranking and are used to test the abnormality of a distribution.
3. True.T1 as an estimator of theta has a smaller variance than T2 hence its more efficient.