Question

Study of aircraft bird strikes. Refer to the InternationalJournal for Traffic and Transport Engineering(Vol. 3,2013) study of aircraft bird strikes at a Nigerian airport,Exercise 6.54 (p. 357). Recall that an air traffic controller

wants to estimate the true proportion of aircraft bird strikesthat occur above 100 feet. Determine how many aircraftbird strikes need to be analyzed to estimate the true proportionto within .05 if you use a 95% confidence interval.

Short answer

227 aircraft bird strikes need to be analyzed to estimate the true proportion to within .05

Step-by-step solution

Given information

Referring to ,Exercise 6.54 (p. 357)

Finding the sample size

Here the sample proportion is$\widehat{p}=\frac{36}{44}=0.82$

$\begin{array}{c}\widehat{q}=1-\widehat{p}\\ =1-0.82\\ =0.18\end{array}$

Here the standard error is 0.05

The critical value for a 95% confidence interval is$z_{\alpha /2}=z_{0.05/2}=z_{0.025}=1.96$

$\begin{array}{c}SE=z_{\alpha /2}\sqrt{\frac{\widehat{p}\widehat{q}}{n}}\\ n={z^2}_{\alpha /2}\frac{\widehat{p}\widehat{q}}{S{E}^2}\\ n={1.96}^2\times \frac{0.82\times 0.18}{{0.05}^2}\\ n=226.81\\ n\approx 227\end{array}$

The required sample size is 227.

227 aircraft bird strikes need to be analyzed to estimate the true proportion to within .05