Question

1. You are interested in estimating the average height in a class of 100 students. In this class the mean height is 65 inches and the standard deviation is 4 inches. You take a sample of size 16 and compute the average (mean) height of the sample which is 64 inches.
   1. If we are sampling with replacement, how many different samples (keeping track of order) of size 16 are possible? (Do not compute this, just explain how to compute it.)
   2. What is the mean of the sampling distribution of sample means when our sample size is 16? Does the answer depend on the sample size?
   3. What is the standard deviation of the sampling distribution of sample means when our sample size is 16? Does the answer depend on the sample size?

Answer 1

Solution:

Population size N = 100

Population Mean = = 65

Population Standard deviation = 4

Sample size n = 16

a)

Suppose that the consequent samples of size 16 are taken with replacement.

N! samples are possible.

i.e. 100! samples are possible.

b)

mean of the sampling distribution of sample means = Population mean

=

So ,

= 65

It does not depend on the sample size.

c)

standard deviation of the sampling distribution of sample means = = 4/16 = 1

= 1

It  depends on the sample size