Question 14 # Analysis of Challenged Referee Calls in a Major Tennis Tournament## IntroductionThis activity involves analyzing the results of challenged referee calls in a major tennis tournament to determine if the gender of the tennis player is independent of whether a call is overturned. We will use a 0.05 significance level for our test.## Null and Alternative HypothesesTo conduct this statistical test, we need to establish our null and alternative hypotheses:- **Option A:** - \( H_0 \): The gender of the tennis player is independent of whether a call is overturned. - \( H_1 \): The gender of the tennis player is not independent of whether a call is overturned.- **Option B:** - \( H_0 \): Male tennis players are more successful in overturning calls than female players. - \( H_1 \): Male tennis players are not more successful in overturning calls than female players.- **Option C:** - \( H_0 \): Male tennis players are not more successful in overturning calls than female players. - \( H_1 \): Male tennis players are more successful in overturning calls than female players.- **Option D:** - \( H_0 \): The gender of the tennis player is not independent of whether a call is overturned. - \( H_1 \): The gender of the tennis player is independent of whether a call is overturned.## Data TableThe table provided gives details on the success of the challenges based on the player's gender:| Gender | Was the Challenge to the Call Successful? | | ||--------|------------------------------------------|---|---|| | Yes | No| || Men | 466 | 738| || Women | 376 | 735| |## Instructions- Determine which option correctly states the null and alternative hypotheses relevant to the data and research question.- Calculate the test statistic based on the data provided to understand the outcome of the hypothesis test.This exercise is intended to help you understand the concept of hypothesis testing and the interpretation of results in the context of real-world data. The accompanying table shows results of challenged referee calls in a major tennis tournament. Use a 0.05 significance level to test the claim that the gender of the tennis player is independent of whether a call is overturned.Click the icon to view the table.---Determine the test statistic:\( \chi^2 = \) [Round to three decimal places as needed.]Determine the P-value of the test statistic:P-value = [Round to four decimal places as needed.]Use a 0.05 significance level to test the claim that the gender of the tennis player is independent of whether a call is overturned. Choose the correct answer below:- A. There is sufficient evidence to warrant rejection of the claim that male tennis players are more successful in overturning calls than female tennis players. - B. There is not sufficient evidence to warrant rejection of the claim that the gender of the tennis player is independent of whether a call is overturned. - C. There is not sufficient evidence to warrant rejection of the claim that male tennis players are more successful in overturning calls than female tennis players. - D. There is sufficient evidence to warrant rejection of the claim that the gender of the tennis player is independent of whether a call is overturned.

The question is about categorical data analysis.Given :To find :Test the claim that the gender of the tennis player is independent of whether a call is overturned. The formula is given bySo,Null and alternative hypothesis :H0 : The gender of the tennis player is independent of whether a call is overturned.H1 : The gender of the tennis player is not independent of whether a call is overturned.Answer : Option ATest statistic :So,Rounding value to 3 decimal places asP value approach :Since the chi square distribution is always right skewed.Using excel command, So,Decision rule :i ) Reject H0 if ii ) Fail to reject H0 if Given : Here, Hence, reject H0Conclusion :There is sufficient evidence to warrant the rejection of the claim that the gender of the tennis player is independent of whether a call is overturned.Answer : Option DNull and alternative hypothesis :H0 : The gender of the tennis player is independent of whether a call is overturned.H1 : The gender of the tennis player is not independent of whether a call is overturned.Answer : Option ATest statistic ( ) = 5.900P value = 0.0151Conclusion :There is sufficient evidence to warrant the rejection of the claim that the gender of the tennis player is independent of whether a call is overturned.Answer : Option D

Math

Statistics

The accompanying table shows results of challenged referee calls in a major tennis tournament. Use a 0.05 significance level to test the claim that the gender of the tennis player is independent of whether a call is overturned. Click the icon to view the table. HTTS Determine the null and alternative hypotheses. OA. Ho: The gender of the tennis player is independent of whether a call is overturned H₁: The gender of the tennis player is not independent of whether a call is overturned. OB. Ho: Male tennis players are more successful in overturning calls than female players. H₁: Male tennis players are not more successful in overturning calls than female players. OC. Ho Male tennis players are not more successful in overturning calls than female players H₁: Male tennis players are more successful in overturning calls than female players. OD. H.: The gender of the tennis player is not independent of whether a call is overturned. H₁ The gender of the tennis player is independent of whether a call is overturned. Determine the test statistic. More Info Men Women 4 Was the Challenge to the Call Successful? Yes 466 376 Print Done No 738 735