## Related questions with answers

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:

$\begin{array}{|c|c|c|c|} \hline \text { One night } & \text { Two nights } & \text { Three nights } & \text { Saturday night } \\ \hline 37 \% & 17 \% & 28 \% & 18 \% \\ \hline \end{array}$

A recent sample of $644$ flights found the following restrictions:

$\begin{array}{|c|c|c|c|} \hline \text { One night } & \text { Two nights } & \text { Three nights } & \text { Saturday night } \\ \hline 117 \% & 137 \% & 298 \% & 92 \% \\ \hline \end{array}$

At the 5% significance level, what is the conclusion to the hypothesis test? Interpret your results.

Solution

VerifiedThe goodness-of-fit test is based on the fact that when the null hypothesis is true, the test statistic follows the $\chi^2$ distribution.

Therefore, the $\textcolor{#4257B2}{\boldsymbol{p}}$**-value** represents the area under the curve of the $\chi^2$ distribution to the right of the test statistic (we have calculated in the part $b.$ that the test statistic is $\chi^2_3=150.39$).

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