Answered: a) If we want to resolve this…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 26PPS

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Some commercial airlines recirculate about half the air in the cabin during flights as a way to improve fuel efficiency. Other airlines make a policy of NOT recirculating the air and instead, have fresh air from the atmosphere constantly being inserted into the cabin with the “old” air being pumped out of the plane. A total of 1100 passengers flying from San Francisco to Denver were used for an experiment. After their flight, they were each given a list of symptoms associated with the common cold. They were asked to report if they experienced cold symptoms within 24 hours of the flight landing. Of the 517 passengers who flew on planes that recirculate the air, 108 reported post-flight cold symptoms. Of the 583 passengers who flew on airlines that do not use recirculation in the cabin, 110 reported symptoms. Suppose now that we want to use the recirculation of air data to explore “Goal #2”, which is to resolve a hypothesis test about . a) If we want to resolve this hypothesis against the alternative that there is some form of difference between the population fractions, then what should the null and alternative hypothesis be? State them each in both symbols AND words. b) In words, what is a Type I error in this scenario? In words, what is a Type II error for this scenario. Which error do you judge to be more severe in its consequences? Or, do you judge the consequences of each error as equal. Explain. Defend yourself. c) Based on your sentences you wrote for part b), pick a significance level . d) Calculate the test statistic needed in order to resolve this hypothesis test. Do not severely round off. Keep MANY decimal places in the calculations. e) Draw a picture that helps with the p-value calculation. f) Find the p-value of this hypothesis test by using either an appropriate chart, Excel code or code built into a graphing calculator. g) Compare your p-value to the significance level . Should you reject the null hypothesis written in part a)? Use a 95% confidence interval to determine if the fraction of flyers for all flights from San Francisco to Denver who experience cold symptoms post-flight is the same no matter the airline air circulation policies.

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