A simple random sample of size n = 56 is obtained from a population that s skewed left with μ=81 and a=8. Does the population need to be normally distributed for the sampling distribution of x to be approximately mormally distributed? Why? What is the sampling distribution of x? Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? OA. No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of x becomes approximately normal as the sample size, n, increases. OB. Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size, n. OC. Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. OD. No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x become approximately normal as the sample size, n, increases. What is the sampling distribution of x? 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.) OA. The sampling distribution of x is approximately normal with μ- = OB. The sampling distribution of x is uniform with μ- = OC. The sampling distribution of x is skewed left with µ = OD. The shape of the sampling distribution of x is unknown with µ and o ■ and o = and o and o
A simple random sample of size n = 56 is obtained from a population that s skewed left with μ=81 and a=8. Does the population need to be normally distributed for the sampling distribution of x to be approximately mormally distributed? Why? What is the sampling distribution of x? Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? OA. No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of x becomes approximately normal as the sample size, n, increases. OB. Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size, n. OC. Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. OD. No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x become approximately normal as the sample size, n, increases. What is the sampling distribution of x? 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.) OA. The sampling distribution of x is approximately normal with μ- = OB. The sampling distribution of x is uniform with μ- = OC. The sampling distribution of x is skewed left with µ = OD. The shape of the sampling distribution of x is unknown with µ and o ■ and o = and o and o
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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![**Educational Resource: Understanding Sampling Distributions and the Central Limit Theorem**
A simple random sample of size \( n = 56 \) is obtained from a population that is skewed left with \( \mu = 81 \) and \( \sigma = 8 \). Does the population need to be normally distributed for the sampling distribution of \( \bar{x} \) to be approximately normally distributed? Why? What is the sampling distribution of \( \bar{x} \)?
---
### Central Limit Theorem: Key Considerations
**Question:** Does the population need to be normally distributed for the sampling distribution of \( \bar{x} \) to be approximately normally distributed? Why?
**Answer Choices:**
- **A.** No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of \( \bar{x} \) becomes approximately normal as the sample size, \( n \), increases.
- **B.** Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of \( \bar{x} \) normal, regardless of the sample size, \( n \).
- **C.** Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases.
- **D.** No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of \( \bar{x} \) become approximately normal as the sample size, \( n \), increases.
---
### Determining the Sampling Distribution
**Question:** What is the sampling distribution of \( \bar{x} \)? Select the correct choice below and fill in the answer boxes within your choice.
- **A.** The sampling distribution of \( \bar{x} \) is approximately normal with \( \mu_{\bar{x}} = \) [ ] and \( \sigma_{\bar{x}} = \) [ ].
- **B.** The sampling distribution of \( \bar{x} \) is uniform with \( \mu_{\bar{x}} = \) [ ] and \( \sigma_{\bar{x}} = \) [ ].
- **C.** The sampling distribution of \( \bar{x} \) is skewed left with \( \mu_{\bar{x}} = \) [ ] and \( \sigma_{\bar{x}} = \) [ ].
- **D.** The](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac3be618-b645-4bd8-855b-808ff3fc18d4%2Fd0fb6050-aa6e-4371-b212-f872a1ee8cbe%2Fomalg_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Resource: Understanding Sampling Distributions and the Central Limit Theorem**
A simple random sample of size \( n = 56 \) is obtained from a population that is skewed left with \( \mu = 81 \) and \( \sigma = 8 \). Does the population need to be normally distributed for the sampling distribution of \( \bar{x} \) to be approximately normally distributed? Why? What is the sampling distribution of \( \bar{x} \)?
---
### Central Limit Theorem: Key Considerations
**Question:** Does the population need to be normally distributed for the sampling distribution of \( \bar{x} \) to be approximately normally distributed? Why?
**Answer Choices:**
- **A.** No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of \( \bar{x} \) becomes approximately normal as the sample size, \( n \), increases.
- **B.** Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of \( \bar{x} \) normal, regardless of the sample size, \( n \).
- **C.** Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases.
- **D.** No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of \( \bar{x} \) become approximately normal as the sample size, \( n \), increases.
---
### Determining the Sampling Distribution
**Question:** What is the sampling distribution of \( \bar{x} \)? Select the correct choice below and fill in the answer boxes within your choice.
- **A.** The sampling distribution of \( \bar{x} \) is approximately normal with \( \mu_{\bar{x}} = \) [ ] and \( \sigma_{\bar{x}} = \) [ ].
- **B.** The sampling distribution of \( \bar{x} \) is uniform with \( \mu_{\bar{x}} = \) [ ] and \( \sigma_{\bar{x}} = \) [ ].
- **C.** The sampling distribution of \( \bar{x} \) is skewed left with \( \mu_{\bar{x}} = \) [ ] and \( \sigma_{\bar{x}} = \) [ ].
- **D.** The
Expert Solution
Step 1: Introduction
Sample size n= 56
μ = 81
σ = 8
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