Question

inspection of a random sample of 25 aircraft showed that 17 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 ± 5 percent?

Answer 1

   The random sample proportion:  

 at 90% confidence interval: The Central 90% of any normal   distribution is: Z_(α/2) = 1.960

   Error = E = ±5% = ±0.05

   Applying the normal distribution theory,

= 0.70 ≤ P≤  0.77(this means that we are 90% confident that the true proportion of jet with wiring problem fall with 0.70 and 0.77, hence there is no need for the airline to conduct further sampling, rather, they should just inspect all the planes)

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