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.
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. $$\begin{array} { l | c c }
& \text { Win } & \text { Loss } \
\hline \text { Suit } & 22 & 28 \
\text { T-Shirt } & 28 & 22
\end{array}$$ What is your conclusion about the null hypothesis?
A)Fail to reject the null hypothesis.
B)Reject the null hypothesis.
C)Fail to support the null hypothesis.
D)Support the null hypothesis.

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.
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. $$\begin{array} { l | c c } 
& \text { Win } & \text { Loss } \
\hline \text { Suit } & 22 & 28 \
\text { T-Shirt } & 28 & 22
\end{array}$$ What is your conclusion about the null hypothesis?
A)Fail to reject the null hypothesis.
B)Reject the null hypothesis.
C)Fail to support the null hypothesis.
D)Support the null hypothesis.

Quizplus · Accepted Answer

The proportions of wins for both groups are close, and without conducting a statistical test (like a chi-square test for independence), we cannot definitively say there is a significant difference. Given the context, failing to reject the null hypothesis means we do not have enough evidence to say the proportions of wins are different for teams wearing suits versus those wearing jeans and t-shirts.

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 $\begin{array} { l | c c } & \text { Win } & \text { Loss } \\\hline \text { Suit } & 22 & 28 \\\text { T-Shirt } & 28 & 22\end{array}$