Question

A testing agency wishes to estimate the mean inflation pressure of official NFL footballs from a known manufacturer. For quality control purposes, the agency wishes to estimate the mean inflation pressure to be within 0.025 pounds of its true value with a 99% confidence interval. What sample size should be specified for this test assuming the standard deviation is estimated to be 0.1 pound?

Enter your answer as a WHOLE NUMBER.▭

Answer 1

To estimate the mean inflation pressure of NFL footballs within 0.025 pounds with a 99% confidence interval and an estimated standard deviation of 0.1 pound, a sample size of 107 is required.

Step-by-step explanation:

The testing agency wishes to estimate the mean inflation pressure of official NFL footballs. The requirement is to estimate the mean to within 0.025 pounds (the margin of error, E) with a 99% confidence interval. The estimated standard deviation (sigma) is 0.1 pound.

To determine the required sample size (n), the z-score corresponding to a 99% confidence level needs to be used, which is approximately 2.576 (from standard z-tables).

The formula to calculate the sample size is: n = (z*sigma/E)^2.

Plugging the values into the formula, we get: n = (2.576*0.1/0.025)^2. This simplifies to n = (2.576*4)^2, which equals n = 10.304^2, and then n = 106.172. Since we cannot have a fraction of a sample, we round up to the nearest whole number, giving us n = 107.

Therefore, the sample size needed for this test is 107.