A large construction company is trying to establish a useful way to view typical profits from jobs obtained from competitive bidding. Because the jobs vary substantially in size and the final amount of the successful bid, the company has decided to express profits as percent earnings:
Percent earnings = 100 × Earnings / Actual construction costs
When money is lost on a project, the earnings are negative and so is the resulting net profit. A sample of 30 jobs yields these percent earnings:
a. Calculate an estimate of the mean percent earnings for the population of jobs or for all potential jobs.
b. Construct a 95% confidence interval for the mean percent earnings for the population of jobs using a large-sample argument.
c. Construct a 95% confidence interval for the mean percent earnings for the population of jobs assuming 30 is a small sample size. What additional assumption do you need to make in this case?
d. Compare the two intervals in parts b and c. Explain why a sample size of 30 is often taken as the cutoff between large and small samples. |

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