15 **Educational Content: Winning Team and Sports Data Analysis**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?**Hypotheses:**- **A.** - \( H_0: \) Basketball games are not more likely to win at home than any other sport. - \( H_1: \) Basketball games are more likely to win at home than any other sport.- **B.** - \( H_0: \) The home/visitor win is dependent on the sport. - \( H_1: \) The home/visitor win is not dependent on the sport.- **C. (Selected Hypothesis)** - \( H_0: \) The home/visitor win is independent of the sport. - \( H_1: \) The home/visitor win is not independent of the sport.- **D.** - \( H_0: \) Basketball games are more likely to win at home than any other sport. - \( H_1: \) Basketball games are not more likely to win at home than any other sport.**Data Table: Winning Team and Sports Data**| | Basketball | Baseball | Hockey | Football ||--------------------|------------|----------|--------|----------|| **Home Team Wins** | 126 | 50 | 50 | 60 || **Visiting Team Wins** | 71 | 49 | 43 | 40 |**Instructions:**Determine the test statistic:\[ \chi^2 = \] (Round to two decimal places as needed.)**Graph Explanation:**The data table provides winning statistics for home and visiting teams across four sports: Basketball, Baseball, Hockey, and Football. For each sport, the number of wins by home teams and visiting teams is listed. This data can be used to analyze whether the sport influences the likelihood of home or visiting teams winning. The task at hand involves using statistical analysis to determine if home/visitor wins are independent of the sport, with a specific emphasis on baseball's potential advantage through modified field dimensions. A 0.05 significance level is to be used for this hypothesis test.**Test Instructions:**1. **Determine the P-Value**: - A space is provided for entering the P-value of the test statistic, which should be rounded to three decimal places as needed.2. **Conclude from the Options**: - After determining the P-value, you'll determine which conclusion is supported: A. **Fail to reject the null hypothesis** - Indicates not enough evidence to say home/visitor wins are dependent on the sport. The data supports that they are independent. B. **Reject the null hypothesis** - Indicates sufficient evidence to say home/visitor wins are dependent on the sport. The data supports this dependency. C. **Reject the null hypothesis** - Similar to B; states there's enough evidence to suggest dependence, so independence is not supported by the data. D. **Fail to reject the null hypothesis** - Similar to A; states there's not enough evidence to suggest dependence. Independence is supported by the data.**Graph/Diagram Explanation:**No specific graphs or diagrams are visible in the text, but a data table is mentioned which can be viewed by clicking an icon, not shown here. This data table presumably contains the results needed for the P-value calculation and subsequent hypothesis testing regarding the independence of home/visitor wins from the sport type.

It is needed to test whether the home/visitor wins are independent of the sport.The null and alternative hypotheses are:H0: The home/visitor win is independent of the sport.H1: The home/visitor win is not independent of the sport.A chi-squared test of association can be used.Consider the below table.BasketballBaseballHockeyFootballRow totalHome Team Wins126505060286Visiting Team Wins71494340203Column Total1979993100489The formula for expected frequency for a cell is,The expected frequencies are:Consider the below table.Observed Frequency (O)Expected Frequency (E)(O – E)2(O – E)2/E126115.2188116.23431.0088135057.901862.438441.0783515054.392619.294930.3547356058.48672.2900770.0391567181.7812116.23431.4212844941.098262.438441.519254338.607419.294930.4997734041.51332.2900770.055165Total--5.98The test statistic is .There are 2 (= r) rows and 4 (= c) columns, The degrees of freedom is df = (r – 1)(c – 1) = (2 – 1)(4 – 1) = 3.The level of significance is α = 0.05.Using the Excel formula =CHISQ.DIST.RT(5.98,3) the P-value is approximately 0.113.The excel output is, Decision rule:If P-value is less than or equal to the level of significance, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.Conclusion:The P-value (= 0.113) is greater than α = 0.05.Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that home/visitor wins are independent of the sport. That is, baseball team is not effective in using the advantage. The theory is not supported by the sample data.The correct option for the hypotheses is C.The null and alternative hypotheses are:H0: The home/visitor win is independent of the sport.H1: The home/visitor win is not independent of the sport.The test statistic is .The P-value is 0.113.The correct option for the conclusion is D."Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that home/visitor wins are independent of the sport. The theory is not supported by the sample data"

Math

Statistics

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. OA. Ho Basketball games are not more likely to win at home than any other sport H₁ Basketball games are more likely to win at home than any other sport. O B. Ho The home/visitor win is dependent on the sport H₁ The home/visitor win is not dependent on the sport. OC. Ho The home/visitor win is independent of the sport H₁ The home/visitor win is not independent of the sport. OD. H Basketball games are more likely to win at home than any other sport H Basketball games are not more likely to win at home than any other sport Determine the test statistic. 2- Winning Team and Sports Data Home Team Wins Visiting Team Wins Basketball Baseball Hockey 126 50 50 71 49 43 Print Football 60 40 Done