Question 13.9: Gender of Train Passengers On a commuter train, the conducto......

Step 1 State the hypotheses and identify the claim.

H_{0} : The passengers board the train at random, according to gender (claim).

H_{1} : The passengers do not board the train at random, according to gender.

Step 2 Determine the critical value. There are 10 \mathrm{M} ‘s and 15 \mathrm{~F} ‘s, so n_{1}=10 and n_{2}=15. Using Table M and \alpha=0.05, the critical value is { }_{18}^{7} which means do not reject H_{0} if the number of runs is between 7 and 18 .

Step 3 Find the test value. Determine the number of runs. Arrange the letters according to runs of males and females, as shown.

\begin{array}{|c|l|} \hline Run & Gender \\ \hline 1 & F F F \\ 2 & M M \\ 3 & F F F F \\ 4 & M \\ 5 & F \\ 6 & M M M \\ 7 & F F F F \\ 8 & M M \\ 9 & F F F \\ 10 & M M \\ \hline \end{array}

There are 10 runs.

Step 4 Make the decision. Compare these critical values with the number of runs. Since the number of runs is 10 and 10 is between 7 and 18 , do not reject the null hypothesis.

Step 5 Summarize the results. There is not enough evidence to reject the hypothesis that the passengers board the train at random according to gender.