Answer to Question #309353 in Statistics and Probability for Chie

Question

Consider all the possible samples of size 2 that can be drawn without replacement from the population 1, 4, 6 and 7.

Compute the following;

a. Mean of the sampling distribution of the sample means

b. Variance of the sampling distribution of the sample means

c. Standard deviation of the sampling distribution of sample means

Answer 1

Sampling distribution of the sample means

a. Mean $=∑xF(x)=4.5$

b. Variance $=∑x^2F(x)-(4.5)^2=22.0002-20.25=1.7502$

c. Standard deviation $=\sqrt{1.7502}=1.3230$