91Ó°ÊÓ

Suppose Jack and Diane are each attempting to use simulation to describe the sampling distribution from a population that is skewed left with mean 50 and standard deviation \(10 .\) Jack obtains 1000 random samples of size \(n=3\) from the population, finds the mean of the 1000 samples, draws a histogram of the means, finds the mean of the means, and determines the standard deviation of the means. Diane does the same simulation, but obtains 1000 random samples of size \(n=30\) from the population. (a) Describe the shape you expect for Jack's distribution of sample means. Describe the shape you expect for Diane's distribution of sample means. (b) What do you expect the mean of Jack's distribution to be? What do you expect the mean of Diane's distribution to be? (c) What do you expect the standard deviation of Jack's distribution to be? What do you expect the standard deviation of Diane's distribution to be?

Suppose you want to study the number of hours of sleep full-time college students at your college get each evening. To do so, you obtain a list of full-time students at your college, obtain a simple random sample of ten students, and ask each of them to disclose how many hours of sleep they obtained the most recent Monday. (a) What is the population of interest in this study? What is the sample? (b) Explain why number of hours of sleep in this study is a random variable. (c) After you obtain your ten observations, you compute the mean number of hours of sleep. Is this a statistic or a parameter? Why? (d) Is the mean number of hours computed in part (c) a random variable? Why? If it is a random variable, what is the source of variation? How does the source of variation in this study differ from that of Problem \(40 ?\)