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.

Answer 2

Using the Central Limit Theorem, it is found that the correct option is:

• a. The expected values of R and S will be equal, and the variability of R will be less than the variability of S.

Central Limit Theorem

• The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation, measuring variability, of $s = \frac{\sigma}{\sqrt{n}}$.

• Hence, a higher sample size leads to less variability.

In this problem:

• The samples are taken from the same population, hence they have the same expected value.

• Due to the higher sample size, R has less variability.

• Hence, option A is correct.

To learn more about the Central Limit Theorem, you can take a look at https://brainly.com/question/25581475