An employee of the Bureau of Transportation Statistics has been given the task of estimating the proportion of on-time arrivals of a budget airline. A prior study has estimated this on-time arrival rate as 78.5%. What is the minimum number of arrivals this employee must include in the sample to ensure that the margin of error for a 95% confidence interval is no more than 0.05?
A) 270
B) 259
C) 260
D) 269

Question

Quizplus · Accepted Answer

The formula for the sample size of a proportion is:n = (Z^2 * p * q) / e^2where:n is the sample sizeZ is the z-score for the desired confidence levelp is the estimated proportion of successesq is the estimated proportion of failures (1 - p)e is the margin of errorIn this case, we have:Z = 1.96 (for a 95% confidence level)p = 0.785q = 1 - p = 0.215e = 0.05Plugging these values into the formula, we get:n = (1.96^2 * 0.785 * 0.215) / 0.05^2= 260.06Therefore, the minimum number of arrivals this employee must include in the sample is 260.

An Employee of the Bureau of Transportation Statistics Has Been