Answer
Step 1:
$H_0$ : The proportions of the on-time performance by the airlines are as follows: 70.8% on time, 8.2% National Aviation System delay, 9.0% because of aircraft arriving late, 12% because of weather conditions and others.
$H_1$: The distribution is not the same as stated in the null hypothesis.
Step 2:
Since α=0.05, and the degrees of freedom are 4-1=3 , the critical value is 7.815.
Step 3:
Expected Value:
0.708 * 200 = 141.6
0.082 * 200 = 16.4
0.09 * 200 =18
0.12 *200 = 24
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$ =$\frac{(125-141.6)^{2}}{141.6}$ + $\frac{(10-16.4)^{2}}{16.4}$ + $\frac{(25-18)^{2}}{18}$
=1.946+2.498+2.722+10.667 + $\frac{(40-24)^{2}}{24}$
=17.832
Step 4:
Since 17.832 > 7.815, the decision is to reject the null hypothesis.
Step 5:
There is enough evidence to reject the claim and conclude that these results differ from the government’s statistics.
