Determine whether the statement is true or false. If it is false, rewrite it as

Question

Determine whether the statement is true or false. If it is false, rewrite it as a true statement.

If the size of a sample is at least 30, then you can use z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution.

Choose the correct choice below.

A. This statement is false. A true statement is, "If the size of a sample is at least 10, then you can use z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution."

B. This statement is false. A true statement is, "There is not any size of a sample that allows you to use z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution."

C. This statement is false. A true statement is, "If the size of a sample is at least 50, then you can use z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution."

D. This statement is true.

Explanation / Answer

If sample size is large enough i.e. at least 30, then using central limit theorem, one can approximate the sampling distribution of sample mean using normal distribution.

So,

If the size of a sample is at least 30, then you can use z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution. (True)

ans-> D. This statement is true.

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