1. Random samples of size n = 2 are drawn from a finite population that consists of the numbers 2, 4, 6, and 8.
(a) Calculate the mean and the standard deviation of this population.
(b) List the six possible random samples of size n=2 that can be drawn from the population and calculate their means.
(c) Use the result of part (b) to construct the sampling distribution of the mean for random samples of size n=2 from the given population.
(d) Calculate the standard deviation of the sampling distribution obtained in part (c) and verify the result by substituting n=2, N=4, and the value of σ obtained in part (a) into the second of the two standard error formulas on page 275.
2. For what positive value of n is the finite population correction factor N-n/N-1 equal to zero?
3. The supervisor of a waste disposal truck that collects waste in a residential neighborhood wants to estimate the mean number of cubic feet of waste collected at these residences. Suppose that the supervisor uses a sample of 30 waste pickups and knows from experience that the standard deviation is 3 cubic feet for such data. Based on the central limit theorem, with what probability can the supervisor assert that the error will be
(a) less than 1 cubic foot:
(b) less than 0.5 cubic foot?
4. During the last week of the semester, students at a certain college spend on the average 4.2 hours using the school's computer terminals with a standard deviation of 1.8 hours. For a random sample of 36 students at that college, find the probabilities that the average time spent using the computer terminals during the last week of the semester is
(a) at least 4.8 hours;
(b) between 4.1 and 4.5 hours.