Chapter 7.1, Problem 2LC

All the possible random samples of size n = 2 are selected from a population with μ = 40 and σ = 10 and the mean is computed for each sample. Then all the possible samples of size n = 25 are selected from the same population and the mean is computed for each sample. How will the distribution of sample means for n = 2 compare with the distribution for n = 25?

1. a. The two distributions will have the same mean and variance.
2. b. The mean and the variance for n = 25 will both be larger than the mean and variance for n = 2.
3. c. The mean and the variance for n = 25 will both be smaller than the mean and variance for n = 2.
4. d. The variance for n = 25 will be smaller than the variance for n = 2 but the two distributions will have the same mean.