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A variable of a population has a mean of u = 82 and a standard deviation of o = 18. a. Identify the sampling distribution of the sample mean for samples of size 36. b. In answering part (a), what assumptions did you make about the distribution of the variable? c. Can you answer part (a) if the sample size is 16 instead of 36? Why or why not? = 82 (Simplify your answer.) What is the standard deviation of the sampling distribution? o: = 2 (Simplify your answer.) b. In answering part (a), what assumptions did you make about the distribution of the variable? O A. No assumptions were made because the sampling distribution is normal, regardless of the distribution of the variable under consideration. O B. It was assumed that the variable was normally distributed. O C. No assumptions were made because, for a relatively large sample size, the sampling distribution is normal, regardless of the distribution of the variable under consideration. O D. It was assumed that the distribution of the variable was unimodal. c. Can you answer part (a) if the sample size is 16 instead of 36? Why or why not? O A. No, because the sample size needs to be at least 30 if the distribution of the variable is unknown. O B. Yes, because the sample size makes no difference in determining the sampling distribution. O C. Yes, because the sample size must be less than 30 if the distribution of the variable is unknown.

A variable of a population has a mean of u = 82 and a standard deviation of o = 18. a. Identify the sampling distribution of the sample mean for samples of size 36. b. In answering part (a), what assumptions did you make about the distribution of the variable? c. Can you answer part (a) if the sample size is 16 instead of 36? Why or why not? = 82 (Simplify your answer.) What is the standard deviation of the sampling distribution? o: = 2 (Simplify your answer.) b. In answering part (a), what assumptions did you make about the distribution of the variable? O A. No assumptions were made because the sampling distribution is normal, regardless of the distribution of the variable under consideration. O B. It was assumed that the variable was normally distributed. O C. No assumptions were made because, for a relatively large sample size, the sampling distribution is normal, regardless of the distribution of the variable under consideration. O D. It was assumed that the distribution of the variable was unimodal. c. Can you answer part (a) if the sample size is 16 instead of 36? Why or why not? O A. No, because the sample size needs to be at least 30 if the distribution of the variable is unknown. O B. Yes, because the sample size makes no difference in determining the sampling distribution. O C. Yes, because the sample size must be less than 30 if the distribution of the variable is unknown.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Problem: Sampling Distribution** A variable of a population has a mean of μ = 82 and a standard deviation of σ = 18. ### a. Identify the sampling distribution of the sample mean for samples of size 36. **Solution:** \[ \mu_{\bar{x}} = 82 \quad (\text{Simplify your answer.}) \] ### What is the standard deviation of the sampling distribution? \[ \sigma_{\bar{x}} = 2 \quad (\text{Simplify your answer.}) \] ### b. In answering part (a), what assumptions did you make about the distribution of the variable? - **A.** No assumptions were made because the sampling distribution is normal, regardless of the distribution of the variable under consideration. - **B.** It was assumed that the variable was normally distributed. - **C.** No assumptions were made because, for a relatively large sample size, the sampling distribution is normal, regardless of the distribution of the variable under consideration. - **D.** It was assumed that the distribution of the variable was unimodal. ### c. Can you answer part (a) if the sample size is 16 instead of 36? Why or why not? - **A.** No, because the sample size needs to be at least 30 if the distribution of the variable is unknown. - **B.** Yes, because the sample size makes no difference in determining the sampling distribution. - **C.** Yes, because the sample size must be less than 30 if the distribution of the variable is unknown. - **D.** No, because the sample size must be less than 5 if the distribution of the variable is unknown. **Answer Choices:** - For part **b.**, option **C** is selected. - For part **c.**, option **A** is selected.
Transcribed Image Text:**Problem: Sampling Distribution** A variable of a population has a mean of μ = 82 and a standard deviation of σ = 18. ### a. Identify the sampling distribution of the sample mean for samples of size 36. **Solution:** \[ \mu_{\bar{x}} = 82 \quad (\text{Simplify your answer.}) \] ### What is the standard deviation of the sampling distribution? \[ \sigma_{\bar{x}} = 2 \quad (\text{Simplify your answer.}) \] ### b. In answering part (a), what assumptions did you make about the distribution of the variable? - **A.** No assumptions were made because the sampling distribution is normal, regardless of the distribution of the variable under consideration. - **B.** It was assumed that the variable was normally distributed. - **C.** No assumptions were made because, for a relatively large sample size, the sampling distribution is normal, regardless of the distribution of the variable under consideration. - **D.** It was assumed that the distribution of the variable was unimodal. ### c. Can you answer part (a) if the sample size is 16 instead of 36? Why or why not? - **A.** No, because the sample size needs to be at least 30 if the distribution of the variable is unknown. - **B.** Yes, because the sample size makes no difference in determining the sampling distribution. - **C.** Yes, because the sample size must be less than 30 if the distribution of the variable is unknown. - **D.** No, because the sample size must be less than 5 if the distribution of the variable is unknown. **Answer Choices:** - For part **b.**, option **C** is selected. - For part **c.**, option **A** is selected.
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