Answer to Question #194574 in Statistics and Probability for yoonie

Question

Solve the following problem, then choose the letter of your answer.

For numbers 1-4: A population consists of five (5) measurements 2, 3, 5, 6, and 7.

Answer the following questions. Show your solution.

1. What is the mean of the population?

A. 4.60 B. 4.92 C. 3.44 D. 5.20

2. What is the variance of the sampling distribution of the sample means with a sample size of 2?

A. 3.90 B. 2.256 C. 2.20 D. 3.44

3. What is the mean of the sampling distribution of the sample means?

A. 4.60 B. 4.92 C. 3.44 D. 5.20

4. What is the variance of the sampling distribution of the sample means?

A. 1.29 B. 4.92 C. 3.44 D. 1.20

5. The population has a standard deviation of 4.9 and has a mean of 28, of the sampling distribution of the sample mean? The sampling distribution was derived with sample size n=4 and all possible samples were drawn with replacements.

𝑨. µ𝒙̅ = 2.45 B. µ𝒙̅ = 1.225 C. µ𝒙̅ = 3.65 D. µ𝒙̅ = 12.005

Answer 1

We have given the population : 2, 3, 5, 6, and 7

1.) Mean of population $= \dfrac{2+3+5+6+7}{5}=4.6$

2.) Sampling distribution of size 2 can be given as:

Variance $= \dfrac{(2.5-4.6)^2+(3.5-4.6)^2+2(4-4.6)^2+2(4.5-4.6)^2+(5-4.6)^2+(5.5-4.6)^2+(6-4.6)^2+(6.5-4.6)^2}{10} \\ = \dfrac{4.41+1.21+0.72+0.02+0.16+0.81+1.96+3.61}{10}\\ = \dfrac{12.9}{10}\\ = 1.29$

c.) Mean of sampling distribution $= \dfrac{46}{10} = 4.6$

d.) Variance = 1.29

e.) Mean remains same for sample $= 28$

Sample standard deviation $= \dfrac{4.9}{\sqrt{4}} = 2.45$