Answer to Question #186668 in Statistics and Probability for Acierlynx

Question

Solve the following problems. Use the properties of the sampling distribution of

sample means.

1. If a population has a mean of 5.7, what is the mean of the sampling distribution

of its means?

2. If a population has a variance of 7.4, what is the variance of the sampling

distribution of its means? The sampling distribution has a sample size of 2

and all possible samples are drawn with replacements.

3. If a population has a standard deviation of 3.2, what is the standard deviation

of the sampling distribution of its means? The sampling distribution has a

sample size of 4 and all possible samples are drawn with replacements.

4. If a population with size of 4 has a variance of 6.8, what is the variance of the

sampling distribution of its means? The sampling distribution has a sample size

of 3 and all possible samples are drawn without replacements.

Answer 1

1. $\mu=5.7$ . The population mean is equal to the mean of the sampling distribution of its means. of its means.
2. $\sigma_x^2=\frac{\sigma^2}{n}$ =$\frac{7.4}{2}$ =3.7
3. $\sigma_x=\frac{\sigma}{\sqrt n}$ =$\frac{3.2}{\sqrt 4}$ =1.6
4. $\sigma_x^2=\frac{\sigma^2}{n}$ =$\frac{6.8}{3}$ =2.67