Winning team data were collected for teams in different sports, with the results given in the table on the top of the next page (based on data from “Predicting Professional Sports Game Outcomes fromIntermediateGame Scores,” by Copper, DeNeve, and Mosteller, Chance,Vol. 5, No. 3–4). Use a 0.10significance level to test the claim that home/visitor wins are independent of the sport. Given that among the four sports included here, baseball is the only sport in which the home team canmodify field dimensions to favor its own players, does it appear that baseball teams are effective in using this advantage?

	Basketball	Baseball	Hockey	Football
Home Team Wins	127	53	50	57
Visiting Team Wins	71	47	43	42

The data for different sports and home/Visiting team wins is provided.

The level of significance 0.10.

The formula forexpected frequencyis,

\(E = \frac{{\left( {row\;total} \right)\left( {column\;total} \right)}}{{\left( {grand\;total} \right)}}\)

The table with row and column total for observed counts is represented as,

Theexpected frequency tableis represented as,

The hypotheses are formulated as,

\({H_0}:\)Home/visitor wins are independent of the sport.

\({H_1}:\)Home/visitor wins are dependent on the sport.

The value of the test statisticis computed as,

\[\begin{aligned}{c}{\chi ^2} = \sum {\frac{{{{\left( {O - E} \right)}^2}}}{E}} \\ = \frac{{{{\left( {127 - 115.9714} \right)}^2}}}{{115.9714}} + \frac{{{{\left( {53 - 58.5714} \right)}^2}}}{{58.5714}} + ... + \frac{{{{\left( {42 - 41.0143} \right)}^2}}}{{41.0143}}\\ = 4.7372\end{aligned}\]

Therefore, the value of the test statistic is 4.7372.

The degrees of freedomare computed as,

\(\begin{aligned}{c}\left( {r - 1} \right)\left( {c - 1} \right) = \left( {2 - 1} \right)\left( {4 - 1} \right)\\ = 3\end{aligned}\)

Therefore, the degrees of freedom are 3.

From the chi-square table, the critical value to 3 degrees of freedom and at 0.10 level of significance 6.2514.

Therefore, the critical value is 6.2514

Since the critical value (6.2514) is greater than the value of the test statistic (4.7372). In this case, the null hypothesis fails to be rejected.

Therefore, the decision is to fail to reject the null hypothesis.

There issufficient evidence to support the claim that Home/visitor wins are independent of the sport.

Thus, the wins are not dependent on the sport.

Thus, the advantage is not effective for the wins of baseball teams.