State whether the following statements are true, false, or uncertain. Justify your answers.
a. An estimator of a parameter is a random variable, but the parameter is non-random, or fixed.
b. An unbiased estimator of a parameter, say, µX, means that it will always be equal to µX.
c. An estimator can be a minimum variance estimator without being unbiased.
d. An efficient estimator means an estimator with minimum variance.
e. An estimator can be BLUE only if its sampling distribution is normal.
f. An acceptance region and a confidence interval for any given problem means the same thing.
g. A type I error occurs when we reject the null hypothesis even though it is false.
h. A type II error occurs when we reject the null hypothesis even though it may be true.
i. As the degrees of freedom (d.f.) increase indefinitely, the t distribution approaches the normal distribution.
j. The central limit theorem states that the sample mean is always distributed normally.
k. The terms level of significance and p value mean the same thing.