Question

A simple random sample of size nequals64 is obtained from a population with muequals43 and sigmaequals8.

Does the population need to be normally distributed for the sampling distribution of x overbar to be approximately normally​ distributed? Why? What is the sampling distribution of x overbar​? Does the population need to be normally distributed for the sampling distribution of x overbar to be approximately normally​ distributed? Why?

A. Yes because the Central Limit Theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x overbar ​normal, regardless of the sample​ size, n.

B. No because the Central Limit Theorem states that regardless of the shape of the underlying​ population, the sampling distribution of x overbar becomes approximately normal as the sample​ size, n, increases.

C. Yes because the Central Limit Theorem states that the sampling variability of nonnormal populations will increase as the sample size increases.

D. 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 overbar become approximately normal as the sample​ size, n, increases.

What is the sampling distribution of x overbar​? 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 x overbar is uniform with mu Subscript x overbarequals nothing and sigma Subscript x overbar = ?

B. The sampling distribution of x overbar follows​ Student's t-distribution with mu Subscript x overbarequals nothing and sigma Subscript x overbar = ?

C. The sampling distribution of x overbar is normal or approximately normal with mu Subscript x overbarequals nothing and sigma Subscript x overbar = ?

D. The sampling distribution of x overbar is skewed left with mu Subscript x overbarequals nothing and sigma Subscript x overbar = ?

Answer 1