A manufacturer of NFL regulation footballs uses a machine to inflate its new balls to a pressure of 13.5 pounds (σ = 0.1).When the machine is properly calibrated,the mean inflation pressure is 13.5 pounds,but uncontrollable factors can cause the pressure of individual footballs to vary.For quality control purposes,the manufacturer wishes to estimate the mean inflation pressure to within 0.025 pounds of its true value with 99 percent confidence.What sample size should be used?

Question

Quizplus · Accepted Answer

We can use the formula for the sample size for estimating a population mean with the desired margin of error and confidence level:

n = (Zα/2 * σ / E)^2

where Zα/2 is the critical value for the desired confidence level (in this case, 99% confidence corresponds to a critical value of 2.58), σ is the population standard deviation (given as 0.1), and E is the desired margin of error (0.025).

Plugging in the values, we get:

n = (2.58 * 0.1 / 0.025)^2
n = 106.584

Since we need a whole number for the sample size, we round up to the nearest integer:

n = 107

Therefore, the manufacturer should use a sample size of 107 to estimate the mean inflation pressure to within 0.025 pounds with 99% confidence. Choice B is the best answer.

A Manufacturer of NFL Regulation Footballs Uses a Machine to Inflate