1) Among college students who hold part-time jobs during the school year, the distribution of the time spent working per week is approximately normally distributed with a mean of 20.20 hours and a standard deviation of 2.60 hours. Let the average time spent working per week for 18 randomly selected college students who hold part-time jobs during the school year. Calculate the mean and the standard deviation of the sampling distribution of , and describe the shape of this sampling distribution.

2) The GPAs of all 5540 students enrolled at a university have an approximately normal distribution with a mean of 3.02 and a standard deviation of .29. Let the mean GPA of a random sample of 48 students selected from this university. Find the mean and standard deviation of , and comment on the shape of its sampling distribution.

3) The GPAs of all students enrolled at a large university have an approximately normal distribution with a mean of 3.02 and a standard deviation of .29. Find the probability that the mean GPA of a random sample of 20 students selected from this university is

a. 3.10 or higher b. 2.90 or lower c. 2.95 to 3.11

4) A company manufactured six television sets on a given day, and these TV sets were inspected for being good or defective. The results of the inspection follow. Good Good Defective Defective Good Good

a. What proportion of these TV sets are good?

b. How many total samples (without replacement) of size five can be selected from this population?

c. List all the possible samples of size five that can be selected from this population and calculate the sample proportion, p, of television sets that are good for each sample. Prepare the sampling distribution of

d. For each sample listed in part c, calculate the sampling error.

5) Brooklyn Corporation manufactures DVDs. The machine that is used to make these DVDs is known to produce 6% defective DVDs. The quality control inspector selects a sample of 150 DVDs every week and inspects them for being good or defective. If 8% or more of the DVDs in the sample are defective, the process is stopped and the machine is readjusted. What is the probability that based on a sample of 150 DVDs, the process will be stopped to readjust the machine?

6) For a population, the value of the standard deviation is 2.65. A sample of 35 observations taken from this population produced the following data.

42 51 42 31 28 36 49 29 46 37 32 27 33 41 47 41 28 46 34 39 48 26 35 37 38 46 48 39 29 31 44 41 37 38 46

a. What is the point estimate of ?

b. Make a 98% confidence interval for .

c. What is the margin of error of estimate for part b?

7) Suppose, for a sample selected from a population is 25.5 and s = 4.9.

a. Construct a 95% confidence interval for assuming n = 47.

b. Construct a 99% confidence interval for assuming n = 47. Is the width of the 99% confidence interval larger than the width of the 95% confidence interval calculated in part a? If yes, explain why.

c. Find a 95% confidence interval for assuming n = 32. Is the width of the 95% confidence interval for with n = 32 larger than the width of the 95% confidence interval for with n =47 calculated in part a? If so, why? Explain.

8) It is said that happy and healthy workers are efficient and productive. A company that manufactures exercising machines wanted to know the percentage of large companies that provide on-site health club facilities. A sample of 240 such companies showed that 96 of them provide such facilities on site.

a. What is the point estimate of the percentage of all such companies that provide such facilities on site?

b. Construct a 97% confidence interval for the percentage of all such companies that provide such facilities on site. What is the margin of error for this estimate?