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

Explanation:

The Central Limit Theorem (CLT) states that if the sample size \(n\geq30\), the sampling distribution of the sample mean \(\bar{x}\) is approximately normal, regardless of the shape of the population distribution. Also, if the population is normal, then the sampling distribution of the sample mean is normal for any sample size \(n\). So the original statement is false.

Answer:

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