Inspection of a random sample of 19 aircraft showed that 15

Inspection of a random sample of 19 aircraft showed that 15 needed repairs to fix a wiring problem that might compromise safety. (a) How large a sample would be needed to estimate the true proportion of jets with the wiring problem, with 90 percent confidence and an error of ± 6 percent? (Enter your answer as a whole number (no decimals). Use a z-value taken to 3 decimal places in your calculations.) Sample size

Solution

Given n =19 ; x = 15

proportion p = 15/19 = 0.789474

q= 0.210526

z value = 1.645

ME=0.06

sample size = [z^2*p*q+ME^2]/ME^2

Sample size required = 126