Question: Suppose the manufacturer of official NFL footballs uses a machine to inflate the new balls to a pressure of 13.5 pounds. For quality control purposes, the manufacturer wishes to estimate the mean inflation pressure to within 0.025 pounds of its true value with a 99% confidence interval. They have now prior knowledge of a population standard deviation so they take a pilot sample of 25 balls, find the inflation pressure and calculate a sample standard deviation of 0.15 pounds. Assuming normality, what total sample size should be specified for this experiment?

b. After examining his budget, the manufacturer decided he can only sample a total of 150 footballs. If he decides to remain 99% confident, how wide does his confidence interval now need to be?

c. If he decides instead that he would rather be within plus or minus 0.025 pounds, how confident would he then be of his estimate?

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