The Ohio Department of Agriculture tested 203 fuel samples across the state in 1999 for accuracy of the reported octane level.For premium grade,14 out of 105 samples failed (they didn't meet ASTM specification and the FTC Octane posting rule).How many samples would be needed to create a 99% confidence interval that is within 0.02 of the true proportion of premium grade fuel-quality failures?

Question

Quizplus · Accepted Answer

We want to find the sample size required to have a 99% confidence interval that is within 0.02 of the true proportion of premium grade fuel-quality failures.

Let p be the true proportion of premium grade fuel-quality failures. Then we want to find n such that:

margin of error = z*(sqrt(p*(1-p)/n)) <= 0.02

where z is the z-score corresponding to a 99% confidence level, which is approximately 2.576.

We don't know the value of p, so we can use the worst-case scenario where p = 0.5, which gives the largest possible margin of error:

2.576*(sqrt(0.5*(1-0.5)/n)) <= 0.02

Simplifying and solving for n, we get:

n >= 1912.74

Since we need a whole number of samples, the smallest sample size that satisfies this inequality is 1913. Therefore, the best choice is C) 1913.

The Ohio Department of Agriculture Tested 203 Fuel Samples Across