A simple random sample of size n= 69 is obtained from a population with µ = 48 and o = 4. Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? ..... D. Yes because 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. 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.) O A. The sampling distribution of x is uniform with µ; = and o, =. O B. The sampling distribution of x is normal or approximately normal with H; = and a-= OC. The sampling distribution of x follows Student's t-distribution with u: = and o = O D. The sampling distribution of x is skewed left with H; = and o=
A simple random sample of size n= 69 is obtained from a population with µ = 48 and o = 4. Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? ..... D. Yes because 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. 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.) O A. The sampling distribution of x is uniform with µ; = and o, =. O B. The sampling distribution of x is normal or approximately normal with H; = and a-= OC. The sampling distribution of x follows Student's t-distribution with u: = and o = O D. The sampling distribution of x is skewed left with H; = 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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Transcribed Image Text:The image contains a question related to the sampling distribution of a statistic from a population. Here's a transcription suitable for an educational website:
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**Question:**
A simple random sample of size n = 69 is obtained from a population with μ = 48 and σ = 4. 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?
**Answer:**
- **Yes**, because 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.
**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 sampling distribution of x̄ is uniform with μₓ̄ = ____ and σₓ̄ = ____.
- B. The sampling distribution of x̄ is normal or approximately normal with μₓ̄ = ____ and σₓ̄ = ____.
- C. The sampling distribution of x̄ follows Student's t-distribution with μₓ̄ = ____ and σₓ̄ = ____.
- D. The sampling distribution of x̄ is skewed left with μₓ̄ = ____ and σₓ̄ = ____.
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This question involves understanding the application of the Central Limit Theorem for the approximation of sampling distributions and choosing the correct statistical model based on given information.
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