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A simple random sample of size n = 36 is obtained from a population that is skewed left with μ = 86 and σ = 2. Does the population need to be normally distributed for the sampling distribution of x̄ to be approximately normally distributed? Why? What is the sampling distribution of x̄? --- **Does the population need to be normally distributed for the sampling distribution of x̄ to be approximately normally distributed? Why?** - **A.** ✔️ No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of x̄ becomes approximately normal as the sample size, n, increases. - **B.** No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x̄ become approximately normal as the sample size, n, increases. - **C.** Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x̄ normal, regardless of the sample size, n. - **D.** Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. **What is the sampling distribution of x̄? Select the correct choice below and fill in the answer boxes within your choice. (Type integers or decimals rounded to three decimal places as needed.)** - **A.** The shape of the sampling distribution of x̄ is unknown with μx̄ = [ ] and σx̄ = [ ]. - **B.** The sampling distribution of x̄ is uniform with μx̄ = [ ] and σx̄ = [ ]. - **C.** The sampling distribution of x̄ is skewed left with μx̄ = [ ] and σx̄ = [ ]. - **D.** The sampling distribution of x̄ is approximately normal with μx̄ = [ ] and σx̄ = [ ].

A simple random sample of size n = 36 is obtained from a population that is skewed left with μ = 86 and σ = 2. Does the population need to be normally distributed for the sampling distribution of x̄ to be approximately normally distributed? Why? What is the sampling distribution of x̄? --- **Does the population need to be normally distributed for the sampling distribution of x̄ to be approximately normally distributed? Why?** - **A.** ✔️ No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of x̄ becomes approximately normal as the sample size, n, increases. - **B.** No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x̄ become approximately normal as the sample size, n, increases. - **C.** Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x̄ normal, regardless of the sample size, n. - **D.** Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. **What is the sampling distribution of x̄? Select the correct choice below and fill in the answer boxes within your choice. (Type integers or decimals rounded to three decimal places as needed.)** - **A.** The shape of the sampling distribution of x̄ is unknown with μx̄ = [ ] and σx̄ = [ ]. - **B.** The sampling distribution of x̄ is uniform with μx̄ = [ ] and σx̄ = [ ]. - **C.** The sampling distribution of x̄ is skewed left with μx̄ = [ ] and σx̄ = [ ]. - **D.** The sampling distribution of x̄ is approximately normal with μx̄ = [ ] and σx̄ = [ ].

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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A simple random sample of size n = 36 is obtained from a population that is skewed left with μ = 86 and σ = 2. Does the population need to be normally distributed for the sampling distribution of x̄ to be approximately normally distributed? Why? What is the sampling distribution of x̄? --- **Does the population need to be normally distributed for the sampling distribution of x̄ to be approximately normally distributed? Why?** - **A.** ✔️ No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of x̄ becomes approximately normal as the sample size, n, increases. - **B.** No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x̄ become approximately normal as the sample size, n, increases. - **C.** Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x̄ normal, regardless of the sample size, n. - **D.** Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. **What is the sampling distribution of x̄? Select the correct choice below and fill in the answer boxes within your choice. (Type integers or decimals rounded to three decimal places as needed.)** - **A.** The shape of the sampling distribution of x̄ is unknown with μx̄ = [ ] and σx̄ = [ ]. - **B.** The sampling distribution of x̄ is uniform with μx̄ = [ ] and σx̄ = [ ]. - **C.** The sampling distribution of x̄ is skewed left with μx̄ = [ ] and σx̄ = [ ]. - **D.** The sampling distribution of x̄ is approximately normal with μx̄ = [ ] and σx̄ = [ ].
Transcribed Image Text:A simple random sample of size n = 36 is obtained from a population that is skewed left with μ = 86 and σ = 2. Does the population need to be normally distributed for the sampling distribution of x̄ to be approximately normally distributed? Why? What is the sampling distribution of x̄? --- **Does the population need to be normally distributed for the sampling distribution of x̄ to be approximately normally distributed? Why?** - **A.** ✔️ No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of x̄ becomes approximately normal as the sample size, n, increases. - **B.** No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x̄ become approximately normal as the sample size, n, increases. - **C.** Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x̄ normal, regardless of the sample size, n. - **D.** Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. **What is the sampling distribution of x̄? Select the correct choice below and fill in the answer boxes within your choice. (Type integers or decimals rounded to three decimal places as needed.)** - **A.** The shape of the sampling distribution of x̄ is unknown with μx̄ = [ ] and σx̄ = [ ]. - **B.** The sampling distribution of x̄ is uniform with μx̄ = [ ] and σx̄ = [ ]. - **C.** The sampling distribution of x̄ is skewed left with μx̄ = [ ] and σx̄ = [ ]. - **D.** The sampling distribution of x̄ is approximately normal with μx̄ = [ ] and σx̄ = [ ].
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