Answer to Question #347460 in Statistics and Probability for Dark

Question

1. A population has a mean of 90 and a standard deviation of a 10. A random sample of 20 is drawn from this population. Find standard deviation of sampling distribution of sample means.

2. Suppose samples of size 10 are drawn from a population consisting of 18 measurements with the mean of 26 and standard deviation of 8. What is the mean of the sampling distribution of sample means?

3. What is the finite population correction factor if the size of the population is 150 and the sample size is 75?

Answer 1

1.

$$\sigma_{\bar{X}}=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{20}}=\sqrt{5}$$

2.

$$\mu_{\bar{X}}=\mu=26$$

3.

$$\sqrt{\dfrac{N-n}{N-1}}=\sqrt{\dfrac{150-75}{150-1}}=\sqrt{\dfrac{75}{149}}\approx0.7095$$