Question

Some commercial airplanes recirculate approximately 50% of the cabin air in order to increase fuel efficiency. The researchers studied 1098 airline passengers, among which some traveled on airplanes that recirculated air and others traveled on planes that did not recirculate air. Of the 517 passengers who flew on planes that did not recirculate air, 106 reported post-flight respiratory symptoms, while 112 of the 581 passengers on planes that did recirculate air reported such symptoms. Is there sufficient evidence to conclude that the proportion of passengers with post-flight respiratory symptoms differs for planes that do and do not recirculate air? Test the appropriate hypotheses using α = 0.05. You may assume that it is reasonable to regard these two samples as being independently selected and as representative of the two populations of interest. (Use a statistical computer package to calculate the P-value. Use p_{do not recirculate} − p_{do recirculate}. Round your test statistic to two decimal places and your P-value to four decimal places.)

z	=
P	=

Is there sufficient evidence? (yes or no)

Answer 1

Given that, of the 517 passengers who flew on planes that did not recirculate air, 106 reported post-flight respiratory symptoms, while 112 of the 581 passengers on planes that did recirculate air reported such symptoms.

That is, n1 = 517 and x1 = 106

n2 = 581 and x2 = 112

significance level $(\alpha)$ = 0.05

The null and the alternative hypotheses are,

$H_0: p_1 - p_2= 0$

$H_a: p_1 - p_2 \neq 0$

Using TI-84 calculator we get,

Test statistic is, z = 0.51

p-value is, p = 0.6113

Here, p-value = 0.6113 > $\alpha =0.05$

So, we fail to reject the null hypothesis ( H₀).

Therefore,

there is not sufficient evidence to conclude that the proportion of passengers with post-flight respiratory symptoms differs for planes that do and do not recirculate air.