91Ó°ÊÓ

Indicate whether the following statements are True or False. The central limit theorem (a) states that, with sufficiently large sample sizes, the shape of the population is normal. (b) states that, regardless of sample size, the shape of the sampling distribution of the mean is normal. (c) ensures that the shape of the sampling distribution of the mean equals the shape of the population. (d) applies to the shape of the sampling distribution-not to the shape of the population and not to the shape of the sample.

Indicate whether the following statements are True or False. The sampling distribution of the mean (a) is always constructed from scratch, even when the population is large. (b) serves as a bridge to aid generalizations from a sample to a population. (c) is the same as the sample mean. (d) always reflects the shape of the underlying population. (e) has a mean that always coincides with the population mean. (f) is a device used to determine the effect of variability, that is, what can happen, just by chance, when samples are random. (g) remains unchanged even with shifts to a new population or sample size. (h) supplies a spectrum of possibilities against which to evaluate the observed sample mean. (i) tends to cluster more closely about the population mean with increases in sample size.

Someone claims that, since the mean of the sampling distribution equals the population mean, any single sample mean must also equal the population mean. Any comment?