31. A study suggests tha t airlines have increased restrictions on cheap fares by raising overnight requirements (The Wall Street Journal, August 19, 2008). This w ould force business travelers to pay more for their flights, since they tend to need the most flexibility and want to be home on weekends. Eight months ago, the overnight stay requirements were as follows:

One night Two nights Three nights Saturday night 37% 17% 28% 18%

A recent sample o f 644 flights found the following restrictions:

One night Two nights Three nights Saturday night 117 137 298 92

a. Specify the competing hypotheses to test whether the recent proportions differ from those cited in the study.

b. Calculate the value o f the test statistic.

c. At a 5% significance level, w hat is the critical value?

d. What is the conclusion to the hypothesis test? Interpret your results.