- 8.5 A market researcher selects a simple random sample of n=100 Twitter users from a population of over 100 million Twitter registered users. After analyzing the sample, she states that she has 95% confidence that the mean time spent on the site per day is between 15 and 57 minutes. Explain the meaning of this statement.
- 8.6 Suppose that you are going to collect a set of data, either from an entire population or from a random sample taken from that population.

a. Which statistical measure would you compute first: the mean or the standard deviation? Explain.

b. What does your answer to (a) tell you about the “practicality” of using the confidence interval estimate formula given in Equation (8.1)? - 8.7 Consider the confidence interval estimate discussed in Problem 8.5. Suppose the population mean time spent on the site is 36 minutes a day. Is the confidence interval estimate stated in Problem 8.5 correct? Explain.
- 8.8 You are working as an assistant to the dean of institutional research at your university. The dean wants to survey members of the alumni association who obtained their baccalaureate degrees five years ago to learn what their starting salaries were in their first full-time job after receiving their degrees. A sample of 100 alumni is to be randomly selected from the list of 2,500 graduates in that class. If the dean’s goal is to construct a 95% confidence interval estimate for the population mean starting salary, why is it not possible that you will be able to use Equation (8.1) on page 279 for this purpose? Explain.
- 8.9 A bottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company. The water bottling company’s specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. A random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 gallon.

a. Construct a 99% confidence interval estimate for the population mean amount of water included in a 1-gallon bottle.

b. On the basis of these results, do you think that the distributor has a right to complain to the water bottling company about the amount of water that the bottles contain? Why?

c. Must you assume that the population amount of water per bottle is normally distributed here? Explain.

d. Construct a 95% confidence interval estimate. How does this change your answer to (b)?

Sample Solution