Question

A study suggests that airlines have increased restrictions on cheap fares by raising overnight requirements (The Wall Street Journal, August 19, 2008). This would 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 of 644 flights found the following restrictions:
One night Two nights Three nights Saturday night
117 137 298 92
1. Calculate the value of the test statistic.
2. At a 5% significance level, what is the critical value?

Answer 1

Test statistic X² = 150.382833

Critical value = 7.815

Explanation:

The hypothesis

H0: true proportion = expected value

H1: at least 1 proportion not equal to expected value

Following the calculations I did in the document attached

The test statistics = 150.382833

To get critical value I used excel

Alpha = 0.05

Degree of freedom = 4-1 = 3

Critical value of X² = 7.815

The decision is to reject H0 if X² > 7.815 and agree with the alternative hypothesis. So we Reject h0 since

150.382833 > 7.815