Question

Some commercial airplanes recirculate approximately 50% of the cabin air in order to increase fuel efficiency. The researchers studied 1100 airline passengers, among which some traveled on airplanes that recirculated air and others traveled on planes that did not recirculate air. Of the 519 passengers who flew on planes that did not recirculate air, 106 reported post-flight respiratory symptoms, while 111 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 = .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 P.)

z = _______(Round the answer to two decimal places.)

P =________ (Round the answer to three decimal places.)

Answer 1

conclusion:There is no sufficient evidence to conclude that the proportion of passengers with post-flight respiratory symptoms differs for planes that do and do not recirculate air at 5% level of significance

Explanation:

Given that the two groups data are as follows:

X favourable N total p proportion T total X total N

Group I 106 516 0.2054 217 1097

Group II 111 581 0.1910

p difference = 0.0144

pooled p = 0.1978

Std error of difference =
`\sqrt{0.1978*0.8021((1)/(519)+(1)/(581) )  }` 0.0262

The value of z is 0.5487.

The value of p is .58232.

The result is not significant at p < .05.

conclusion:There is no sufficient evidence to conclude that the proportion of passengers with post-flight respiratory symptoms differs for planes that do and do not recirculate air at 5% level of significance