State whether the following statements are True or False. Give reasons in support of your answer:

(i) If the form of the population is not known and data are in ordinal form then we apply the Wilcoxon Signed rank test for testing hypothesis about average.

(ii) The Neyman-Pearson lemma provides the most powerful test of size a for testing a simple hypothesis against a simple alternative hypothesis.

(iii) The Rao-Blackwell theorem enables us to obtain a manimum variance unbiased estimator through complete statistic.

(iv) For testing goodness of fit when the data are in categorical form, we use K-S test.

(v) In the Bayesian approach, we treat the parameter as a constant.

(b) Differentiate between Rao-Blackwell and Lehmann-Scheffe theorems.

(i) False: The Wilcoxon Signed Rank test is typically used for paired data where the population distribution is not necessarily normal, but for testing hypotheses about medians, not averages. When the data is ordinal, the test is appropriate for median-related hypotheses, not specifically for the average.

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