5. In 2006, tenis introduced a challenge system in which a player can challenge a decision as to whether a tennis ball was correctly called 'in’ or ´ouť by an official. In the 2015 U.S. Open Tennis...

Extracted text: 5. In 2006, tenis introduced a challenge system in which a player can challenge a decision as to whether a tennis ball was correctly called 'in’ or ´ouť by an official. In the 2015 U.S. Open Tennis Championship there were a total of 850 player challenges between both the Men's and Women's Singles matches. These challenges were determined either to be correct (meaning the player was correct and the umpire was incorrect) or incorrect (meaning the player was incorrect and the umpire was correct). These 850 challenges are summarized in the table below. Player Challenge Men's Women's Correct 153 72 Incorrect 394 231 (a) Calculate the proportion of all challenges that were determined to be correct. (b) Using these data as a representative sample of all player challenges in professional tennis, a 95% confidence interval for the difference in the proportion of men's and women's challenges that are determined to be correct (men – women) was found to be 0.04 ± 0.06. All conditions for inference were met. Does this confidence interval provide convincing statistical evidence that there is a difference in the effectiveness with which men and women use the challenge system? Justify your answer. -8- A scientific study has demonstrated that the best time for a player to use a challenge is when the tennis ball was called 'out' but the player believes that the ball was actually ʻin’ because when objects travel faster than the human eye the umpire is left to fill the gap with their own perception. The table below shows the Women's Singles challenges based on if the tennis ball was called ´out’ or 'in. Umpire Called Ball Out Umpire Called Ball In Player Challenge Correct 61 11 Incorrect 111 120 (c) Calculate the proportion of correct player challenges when the umpire called the ball 'out' and the proportion of correct player challenges when the umpire called the ball 'in.’ Out proportion: In proportion: (d) Using these data as a representative sample of all player challenges in professional tennis, a 95% confidence interval for the difference in the proportion of correct challenges when the umpire calls the ball 'out’ and when the umpire calls the ball 'in’ (out - in) was found to be 0.27 ± 0.09. All conditions for inference were met. Does this confidence interval provide statistical evidence to support the scientific findings detailed above? Justify your answer.