IPOs—initial public offerings of stock—create billions of dollars of new wealth for owners, managers, and employees of companies that were previously privately owned. Nevertheless, hundreds of large and thousands of small companies remain privately owned. The revenues of a random sample of 15 firms from Forbes 228 Largest Private Companies list are given in the table 

a. Describe the population from which the random sample was drawn.

b. Use a 98% confidence interval to estimate the mean revenue of the population of companies in question.

c. Interpret your confidence interval in the context of the problem.

d. What characteristic must the population possess to ensure the appropriateness of the estimation procedure used in part b?

e. Suppose Forbes reports that the true mean revenue of the 228 companies on the list is $5.0 billion. Is the claim believable?

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Company Staples Pilot Flying J Tenaska Energy Wawa Gulf States Toyota Brookshire Grocery Sinclair Oil Bose Mary Kay Drummond Petco SAS Forever 21 Rock Ventures Conair Revenue (in billions) $14.0 29.0 11.9 12.1 9.2 2.5 5.0 3.9 3.6 2.0 4.0 3.3 2.7 6.7 2.0