Question

determine whether the statement is true or false. if it is false, rewrite it as a true statement.
a sampling distribution of a sample mean is normal only if the population is normal.

choose the correct answer below.
a. the statement is false. a sampling distribution of a sample mean is approximately normal if either ( ngeq30 ) or the population is normal.
b. the statement is true.
c. the statement is false. a sampling distribution of a sample mean is approximately normal only if ( ngeq30 ).
d. the statement is false. a sampling distribution of a sample mean is never normal.

Explanation:

The Central Limit Theorem states that if the population is normal, the sampling distribution of the sample mean is normal. Also, if the sample size \(n\geq30\), the sampling distribution of the sample mean is approximately normal (even if the population is not normal). So the original statement is false as it ignores the \(n\geq30\) case.

Answer:

A. The statement is false. A sampling distribution of a sample mean is approximately normal if either \(n\geq30\) or the population is normal.