State whether the following statements are True or False. Give reason in support of your answer: (5×2=10)

(a) If the probability of non rejection of H₀ when H₁ is true is 0.4 then power of the test will be 0.6.

(b) If T₁ and T₂ are two estimators of the parameter θ such that Var(T₁) = 1/n and Var(T₂) = n then T₁ is more efficient than T₂.

(c) A 95% confidence interval is smaller than 99% confidence interval.

(d) 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.

(e) Non parametric tests are more powerful than the parametric tests.

a) We reject the null hypothesis in favor of the alternative hypothesis if the sample evidence suggests so. If the sample does not contradict H0, we continue to believe it is true. Thus, the two possible conclusions from a hypothesis-testing analysis are reject H0 or fail to reject H0. The power of a test is the probability of rejecting the null hypothesis when it ____ _________ ______ ________ ______.
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