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 515 passengers who flew on planes that did not recirculate air, 106reported post-flight respiratory symptoms, while 111 of the 583 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 ? = 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	=

Answer 1

Here by the problem,

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

So among the samples the proportion of passengers on planes that showed posy flight respiratory symptoms, on the plane that did not and did recirculate air respectively are,

SO if we assume as the the proportions of passengers with post-flight respiratory symptoms for planes that do not and do recirculate air, and we want to test that if there is sufficient evidence to conclude that the proportion of passengers with post-flight respiratory symptoms differs for planes that do not and do recirculate air

Then the appropriate hypotheses for 0.05 level of significance be,

Here we assume that it is reasonable to regard these two samples as being independently selected and as representative of the two populations of interest.

So here the pooled proportion of respiratory problem is,

So in order to test that the test statistic be,

where under null hypothesis, z~N(0,1)

So putting the values we get,

Hence the p-value be,

So as p-value=0.5217>0.05=level of significance hence based on data we fail to reject null hypothesis and conclude that 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.

Hence the answer.............

Thank you............