Question

True or false and please explain

Answer 1

A. False. The first part of the statement is true, but the second part is not. The sample mean is not always equal to the population mean. The sample mean will vary (it's a random variable).

B. True. The larger the sample, the better the estimate. Ideally we would take a census, but that is often too costly. The next best thing is to select a sample that is of the proper size.

C. True. Consider a normal distribution with mean mu and standard deviation sigma. The distribution of sample means, aka xbar distribution, will have mean mu and standard deviation sigma/sqrt(n), where n is the sample size. We see that sigma/sqrt(n) is smaller than sigma. This tells the xbar distribution is much taller and more narrow compared to the normal distribution.