(a) By the Central Limit Theorem, if X1, . . . , Xn is an iid sample from a population with mean and variance 2 , then X is approximately Normally distributed with mean and variance 2/n.

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(b) By saying an estimator for is unbiased, we mean that converge to in probability as sample size increases.

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(c) If is unbiased for , we have MSE() = Var().

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(d) In a testing procedure for H0 : = 0 at significance level , the probability of not rejecting H0 when = 0 were true, is 1 1 .

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(e) Let X1, . . . , Xn be iid from N(, 2 ). Then as n increases, the length of 95% confidence interval for increases.

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(f) If the null hypothesis is rejected in a test procedure, then it is possible that a type I error is made.

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(g) In ANOVA F-test for H0 : 1 = 2 = 3, we should assume that 21 = 22 = 23.

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(h) If H0 : 1 = 2 = 3 is rejected in ANOVA F-test, we can conclude that we have statistical evidence to say that all three means are different from one another.

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(i) After rejecting ANOVA F-test of H0 : 1 = 2 = 3 = 4 at significance level , one may continue two-sample t-tests for each pairs using the same significance level to maintain family-wise Type I error rate.

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(j) If X1, . . . , Xn is an iid sample from a population with finite mean and variance, X approaches to Normal distribution as the sample size increases, and the required sample size is also the same regardless of the shape of the population distribution.

Choose: T F