91影视

The International Journal for Traffic and Transport Engineering reported on a study of aircraft bird strikes at Aminu Kano International Airport in Nigeria, a sample of 44 aircraft bird strikes was analyzed.

The researchers found that 36 of the 44 bird strikes at the airport occurred above 100 feet.

The sample proportion is the point estimator of the population proportion p.

The sample proportion is,

$\begin{array}{rcl}\hat{\mathrm{p}}& =& \frac{\mathrm{X}}{\mathrm{n}}\\ & =& \frac{36}{44}\\ & =& 0.8182\end{array}$

Then the level of$100\left(1-\mathrm{伪}\right)\%$ confidence interval for p (proportion) is,

$\hat{\mathrm{p}}卤{\mathrm{z}}_{\frac{\mathrm{伪}}{2}}\sqrt{\frac{\hat{\mathrm{p}}\left(1-\hat{\mathrm{p}}\right)}{\mathrm{n}}}$

For a 95% confidence interval, the value of$\frac{\mathrm{伪}}{2}$ is,

$\begin{array}{rcl}100\left(1-\mathrm{伪}\right)\%& =& 95\%\\ \left(1-\mathrm{伪}\right)& =& 0.95\end{array}$

For,$\mathrm{伪}=0.05\mathrm{and}\frac{\mathrm{伪}}{2}=0.025$

The 95% confidence interval is,

$\begin{array}{rcl}\hat{\mathrm{p}}卤{\mathrm{z}}_{\frac{\mathrm{伪}}{2}}\sqrt{\frac{\hat{\mathrm{p}}\left(1-\hat{\mathrm{p}}\right)}{\mathrm{n}}}& =& 0.8182卤1.960\sqrt{\frac{0.8182\left(1-0.8182\right)}{44}}\left[\mathrm{From}\mathrm{Standard}\mathrm{Normal}\mathrm{Table}\right]\\ & =& \left(0.8182卤1.960\sqrt{0.0034}\right)\\ & =& \left(0.8182卤0.1143\right)\\ & =& \left(0.7039,0.9325\right)\end{array}$

Here the 95% confidence interval for the aircraft bird strikes occurs is (0.704, 0.933),an airport air traffic controller estimates that less than 70% of aircraft bird strikes occur above 100 feet. So here the estimate is outside of the 95% confidence interval.

So, at a 5% level of significance, it can be concluded that the estimate is not good.