Some commercial airplanes recirculate approximately 50% of the cabin air in order to increase fuel efficiency. The authors of the paper €œAircraft Cabin Air Recirculation and Symptoms of the Common Cold€ (Journal of the American Medical Association [2002]: 483€“486) studied 1,100 airline passengers who flew from San Francisco to Denver. Some passengers 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, 108 reported post-flight respiratory symptoms, while 110 of the 583 passengers on planes that did recirculate air reported such symptoms. The question of interest is whether the proportions of passengers with post-flight respiratory symptoms differ for planes that do and do not recirculate air. 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.
a. What hypotheses should be tested to answer the question of interest?
b. Are the two samples large enough for the large-sample test for a difference in population proportions to be appropriate?
c. Based on the following Minitab output, what is the value of the test statistic and what is the value of the associated P-value? If a significance level of 0.01 is selected for the test, will you reject or fail to reject the null hypothesis?
Test and CI for Two Proportions

Difference = p (1) - p (2)
Estimate for difference: 0.0202182
95% CI for difference: (-0.0270743, 0.0675108)
Test for difference = 0 (vs not = 0): Z = 0.84
P-Value = 0.401
d. Interpret the result of the hypothesis test in the context of this problem.

Transcribed Image Text:

Sample X 108 N Sample p 517 0.208897 110 583 0188679