State whether the following statements are True or False. Give reason in support of your answer.
a) If probability density function of a t-distribution is

f(t) = 1/ π (1+t2) ; - ∞ <t< ∞
then degrees of freedom of the distribution will be 1.
b) If T1 and T2 are two estimators of an parameter θ such that Var(T1) = 1/2n and Var(T2) = 2/n then T1 is more efficient than T2.
c) If the probability of non rejection of H0 when H1 is true is 0.4 then power of the test will be 0.6.
d) The Wilcoxon signed-rank test is more powerful than the sign test.
e) The t-test is used for testing the independence of two attributes.

a) False. The probability density function provided is that of the Cauchy distribution, which does not have degrees of freedom. The degrees of freedom in a t-distribution are a parameter that determines the shape of the distribution, and typically _____ ___ _______ ________ _________ _______ ________ ____ ______ _____ ________.
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