Question

Winning team data were collected for teams in different sports, with the results given in the accompanying table. Use a 0.05 significance 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 can modify field dimensions to favor its own players, does it appear that baseball teams are effective in using this advantage? Click the icon to view the data table Winning Team and Sports Data

Answer 1

To test the claim that home/visitor wins are independent of the sport, a chi-square test for independence can be used. This test will determine if there is a significant association between the two categorical variables. The expected frequencies are calculated to compare with the observed frequencies and compute the chi-square test statistic.

Step-by-step explanation:

To test the claim that home/visitor wins are independent of the sport, we can use a chi-square test for independence. This test will allow us to determine if there is a significant association between the two categorical variables: home/visitor wins and sport.

We need to set up the null and alternative hypotheses:

• Null hypothesis (H0): Home/visitor wins are independent of the sport.
• Alternative hypothesis (Ha): Home/visitor wins are not independent of the sport.

Next, we calculate the expected frequencies for each cell in the contingency table under the assumption of independence. We can use the formula:

Expected Frequency = (Row Total × Column Total) / Grand Total

Once we have the expected frequencies, we can compute the chi-square test statistic using the formula:

Chi-square = Σ ((Observed Frequency - Expected Frequency)² / Expected Frequency)

Finally, we compare the chi-square test statistic to the critical value from the chi-square distribution with (m-1)(n-1) degrees of freedom, where m is the number of rows and n is the number of columns in the contingency table.

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a significant association between home/visitor wins and sport.