Question

which of the following statements about the sampling distribution of the sample mean, x - bar, is true? check all that apply. a. the distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough. b. the distribution is normal regardless of the sample size, as long as the population distribution is normal. c. the distributions mean is the same as the population mean. d. the distributions standard deviation is smaller than the population standard deviation. select all that apply. 10 points

Explanation:

• A is true by Central Limit Theorem.
• B is true for normal populations.
• C is a property of sampling - distribution of sample mean.
• D is true as standard deviation of sample mean is $\frac{\sigma}{\sqrt{n}}$.

Answer:

A. The distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough.
B. The distribution is normal regardless of the sample size, as long as the population distribution is normal.
C. The distribution's mean is the same as the population mean.
D. The distribution's standard deviation is smaller than the population standard deviation.