Question

A certain statistic will be used as an unbiased estimator of a parameter. Let R represent the sampling distribution of the estimator for samples of size 35, and let S represent the sampling distribution of the estimator for samples of size 15. Which of the following must be true about R and S?
a. The expected values of R and S will be equal, and the variability of R will be less than the variability of S.
b. The expected values of R and S will be equal, and the variability of R will be equal to the variability of S.
c. The expected values of R and S will be equal, and the variability of R will be greater than the variability of S.
d. The expected value of R will be greater than the expected value of S, and the variability of R will be greater than the variability of S.
e. The expected value of R will be greater than the expected value of S, and the variability of R will be less than the variability of S.

Answer 1

Answer:

c. The expected values of R and S will be equal, and the variability of R will be greater than the variability of S.

Step-by-step explanation:

This is Central Limit Theorem concept in which independent variables are added and form a normal distribution. The random sample of n sample size is selected which calculates normally distributed mean and variance. The expected value of samples distributor will be higher than the sample distribution.