At a high school debate tournament, half of the teams were asked to wear suits and ties and the rest were asked to wear jeans and t-shirts. The results are given in the table below. In order to test the claim at the 0.05 level that
The proportion of wins is the same for teams wearing suits as for teams wearing jeans, what would the null
Hypothesis be? $$\begin{array} { l | c c }
& \text { Win } & \text { Loss } \
\hline \text { Suit } & 22 & 28 \
\text { T-Shirt } & 28 & 22
\end{array}$$
A) The mean number of wins is different for teams wearing suits as for teams wearing jeans.
B) The proportions of wins is the same for teams wearing suits as for teams wearing jeans.
C) The proportions of wins is different for teams wearing suits as for teams wearing jeans.
D) The mean number of wins is the same for teams wearing suits as for teams wearing jeans.

Question

At a high school debate tournament, half of the teams were asked to wear suits and ties and the rest were asked to wear jeans and t-shirts. The results are given in the table below. In order to test the claim at the 0.05 level that
The proportion of wins is the same for teams wearing suits as for teams wearing jeans, what would the null
Hypothesis be? $$\begin{array} { l | c c } 
& \text { Win } & \text { Loss } \
\hline \text { Suit } & 22 & 28 \
\text { T-Shirt } & 28 & 22
\end{array}$$
A) The mean number of wins is different for teams wearing suits as for teams wearing jeans.
B) The proportions of wins is the same for teams wearing suits as for teams wearing jeans.
C) The proportions of wins is different for teams wearing suits as for teams wearing jeans.
D) The mean number of wins is the same for teams wearing suits as for teams wearing jeans.

Quizplus · Accepted Answer

The null hypothesis should state that there is no difference in the proportion of wins between teams wearing suits and teams wearing jeans, which is exactly what choice B says. The other choices (A and D) are not relevant to this situation since we are comparing proportions, not means, and we are interested in wins, not just the number of wins. Choice C is close, but it states that the proportions are different, when in fact we want to test if they are the same.

At a High School Debate Tournament, Half of the Teams Win Loss Suit 2228 T-Shirt 2822\begin{array} { l | c c } & \text { Win } & \text { Loss } \\\hline \text { Suit } & 22 & 28 \\\text { T-Shirt } & 28 & 22\end{array} Suit T-Shirt ​ Win 2228​ Loss 2822​​

At a High School Debate Tournament, Half of the Teams $\begin{array} { l | c c } & \text { Win } & \text { Loss } \\\hline \text { Suit } & 22 & 28 \\\text { T-Shirt } & 28 & 22\end{array}$