Which of the following statements is (are) true with respect the to sampling dis

Question

Which of the following statements is (are) true with respect the to sampling distribution of sample means?

a. When the population has a normal distribution, the sampling distribution of the sample mean is normally distributed for any sample size.

b. When the population has a arbitrary distribution, the sampling distribution of the sample mean is normally distributed for any sample size

c. In most applications, the sampling distribution of can be approximated by a normal distribution whenever the sample is size 30 or more

d. In cases where the population is highly skewed or outliers are present, samples of size 30 are sufficient

e. In cases where the population is highly skewed or outliers are present, samples of size 50 may be needed

Explanation / Answer

Statement a and c are true. i.e.,

a. When the population has a normal distribution, the sampling distribution of the sample mean is normally distributed for any sample size.

c. In most applications, the sampling distribution of can be approximated by a normal distribution whenever the sample is size 30 or more.

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