Section 8.1 Homework Question 3 Answer

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Section 8.1 Homework 

3.  A simple random sample of size n=40 is obtained from a population with ì=64 and ó=9. 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​?Does the population need to be normally distributed for the sampling distribution of x to be approximately normally​ distributed? Why?

  1. No because 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.
  2. 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.
  3. No because 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.
  4. Yes because 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 x​?

Select the correct choice below and fill in the answer boxes within your choice.

The sampling distribution of is skewed left with nothing and nothing.

The sampling distribution of follows Student’s t-distribution with nothing and nothing.

The sampling distribution of is normal or approximately normal with 64 and 1.423.

The sampling distribution of is uniform with nothing and nothing.

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This question is taken from Math 136 – Introduction to Statistics » Summer 2021 » Section 8.1 Homework