Suppose that a new diet barely works and that if everyone in the population of overweight adults were to follow it, the weight losses would be bell-shaped with a mean of 0.1 pound and a standard deviation of 5 pounds.
a. Describe the sampling distribution of the sample mean for n = 100.
b. Find the standardized statistic corresponding to a sample mean weight loss of 1 pound.
c. Using your answer in part (b), comment on whether a sample mean of 1 pound would be unusual in this situation.
d. Now suppose that the sample size is increased to n = 900. Repeat parts (a), (b), and (c) in that case. In particular, comment on whether a sample mean of 1 pound would be unusual.
e. Compare your answers to parts (c) and (d). Use the comparison to make a general statement about how sample size affects standardized statistics related to the sampling distribution of the sample mean.