State whether the following statements are true or false and also give the reason in support of your answer:

a) If X and Y are uncorrelated, the V(Rag) reduces to that of Variance of Ratio Estimator of Population mean

b) Among all the members of the General Class of the estimators only Regression estimator is an unbiased estimator of the Population mean.

c) An Incomplete Block Design with the following parameters b=8,k=3,9=8,r=3 is found to be a Balanced Incomplete Block Design.

d) A One-half fractional factorial design of a 2ª full factorial design will be denoted by a 22 Factorial design.

e) The Cluster estimator ỹ, becomes an unbiased estimator of population mean only if M and , are uncorrelated

a) True
If XX and YY are uncorrelated, the covariance term in the variance of the regression estimator becomes zero. In such a case, the variance of the regression estimator (V(Rag)) simplifies and becomes equivalent to the variance of the ratio estimator, hence V(Rag) reduces to that of the Variance of Ratio Estimator of the population mean.

b) False
Among all the members of the general class of estimators, the regression estimator is generally biased, although ________ ____ ________ _________ _________ ___.
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