TI-83/84 PLUS Winning team data were collected for teams in different sports, with the results given in the table below. Use the TI-83/84 Plus results at a 0.05 level of significance to test the claim that home/visitor wins are independent of the sport. x² - Test x² = 11.283947924 P=0.0102854951 df = 3 Basketball Baseball 82 Hockey 78 Football 47 Home team wins 141 Visiting team wins 61 39 38 46 the null hypothesis that home/visitor wins are independent of the sport. It appears that the home-field advantage Reject depend on the sport.

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### Analysis of Home vs. Visitor Wins Across Different Sports

Winning team data were collected for teams in different sports, with the results given in the table below. Use the TI-83/84 Plus results at a 0.05 level of significance to test the claim that home/visitor wins are independent of the sport.

#### Data Table: 

| Wins              | Basketball | Baseball | Hockey | Football |
|-------------------|------------|----------|--------|----------|
| Home team wins    | 141        | 82       | 78     | 47       |
| Visiting team wins| 61         | 39       | 38     | 46       |

#### TI-83/84 Plus Results: 
- χ² - Test
- χ² = 11.283947924
- P = 0.0102854951
- df = 3

#### Conclusion Options:
Using the data and χ² test results, select the appropriate conclusion from the options provided.

- **Conclusion:**
  - [ ] Reject 
  - [ ] Fail to reject 

the null hypothesis that home/visitor wins are independent of the sport. It appears that the home-field advantage [ ]  depend on the sport.

Here, examining the p-value from the χ² test, which is 0.0102854951, and comparing it to the significance level of 0.05, we can make a conclusion about the hypothesis.

#### Explanation of Graph/Chart:
The table provides the number of wins for home teams and visiting teams across four different sports: Basketball, Baseball, Hockey, and Football. The number of wins are listed under the corresponding sports, showing a comparison between home and visitor wins. 

The results computed using the TI-83/84 Plus calculator present:
- A χ² value of 11.283947924
- A p-value of 0.0102854951
- Degrees of freedom being 3

These statistical values are used to determine whether the difference in wins is statistically significant across different sports or if they occur by random chance. The low p-value indicates that there is a significant relationship between the sport and the likelihood of home or visitor wins, leading us to reject the null hypothesis. This implies that the home-field advantage does depend on the sport.
Transcribed Image Text:### Analysis of Home vs. Visitor Wins Across Different Sports Winning team data were collected for teams in different sports, with the results given in the table below. Use the TI-83/84 Plus results at a 0.05 level of significance to test the claim that home/visitor wins are independent of the sport. #### Data Table: | Wins | Basketball | Baseball | Hockey | Football | |-------------------|------------|----------|--------|----------| | Home team wins | 141 | 82 | 78 | 47 | | Visiting team wins| 61 | 39 | 38 | 46 | #### TI-83/84 Plus Results: - χ² - Test - χ² = 11.283947924 - P = 0.0102854951 - df = 3 #### Conclusion Options: Using the data and χ² test results, select the appropriate conclusion from the options provided. - **Conclusion:** - [ ] Reject - [ ] Fail to reject the null hypothesis that home/visitor wins are independent of the sport. It appears that the home-field advantage [ ] depend on the sport. Here, examining the p-value from the χ² test, which is 0.0102854951, and comparing it to the significance level of 0.05, we can make a conclusion about the hypothesis. #### Explanation of Graph/Chart: The table provides the number of wins for home teams and visiting teams across four different sports: Basketball, Baseball, Hockey, and Football. The number of wins are listed under the corresponding sports, showing a comparison between home and visitor wins. The results computed using the TI-83/84 Plus calculator present: - A χ² value of 11.283947924 - A p-value of 0.0102854951 - Degrees of freedom being 3 These statistical values are used to determine whether the difference in wins is statistically significant across different sports or if they occur by random chance. The low p-value indicates that there is a significant relationship between the sport and the likelihood of home or visitor wins, leading us to reject the null hypothesis. This implies that the home-field advantage does depend on the sport.
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