Inspection of a random sample of 24 aircraft showed that 16 needed repairs to fi

Question

Inspection of a random sample of 24 aircraft showed that 16 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 plusminus 4 percent? (Enter your answer as a whole number (no decimals). Use a z-value taken to 3 decimal places in your calculations.) Sample size (b) Would the amine actually conduct further sampling, or just inspect all the planes? Conduct further sampling Inspect all the planes

Explanation / Answer

p = 16/24 = 0.67 , q = 0.23 ,

z value at 90% confidence interval = 1.645

Margin of error = z * sqrt(p*q/n)

0.04 = 1.645 * sqrt(0.67 * 0.23 / n)

n = 260.62

n = 261

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