Inspection of a random sample of 27 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 98 percent confidence and an error of ± 8 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 airline actually conduct further sampling, or just inspect all the planes?  Conduct further samplingInspect all the planes

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Asked Sep 29, 2019
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Inspection of a random sample of 27 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 98 percent confidence and an error of ± 8 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 airline actually conduct further sampling, or just inspect all the planes?
  

  • Conduct further sampling
  • Inspect all the planes
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Expert Answer

Step 1

(a) It is provided that a random sample, n of 27 aircraft showed that 16, x needed repairs to fix wiring problem. The margin of error is ±8 percent. The confidence level is 98%. Therefore, the level of significance is 1 – confidence level = 2% or 0.02.

The sample proportion is,

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х р- п 16 27 0.5925

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Step 2

The required sampl...

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Za P(1-p) п E2 2 Z0.02 0.5925(1-0.5925) 0.082 (20.01) 0.5925 (10.5925) 0.082 (2.326) 0.5925 (1-0.5925) 0.082 (Using standard normal table) - 204.10 204

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