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 515 passengers who flew on planes that did not recirculate air, 106 reported post-flight respiratory symptoms, while 112 of the 585 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 pdo not recirculate − pdo recirculate. Round your test statistic to two decimal places and your P-value to four decimal places.)

Answer 1

Let we call the sample which do not recirculate as 1 and the other as 2.

Then our hypotheses are, '

Vs.,

From the data given,

= 106/515= 0.2058

= 112/585 = 0.1915

and the pooled proportion is,

= 0.1982

Since the two groups are independent, we can use the z-test to test oue claim.

z= = 0.60

Now, from z-table, P-value = 0.5507, i.e., p-value>0.05.

Since the p-value is very high, we fail to reject the null hypothesis.

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.