A basketball coach claims that the team's players commit, on average, no more than 10 fouls per game. Let \( \mu \) represent the team's average number of fouls per game. Another coach thinks that these players create more fouls. What is the null hypothesis, \( H_{0} \), for this situation? \( \mu<10 \) \( \mu \leq 10 \) \( \mu>10 \) \( \mu \geq 10 \) COMPLETE What is the alternative hypothesis, \( \mathrm{H}_{\mathrm{a}} \). for this situation? \( \mu<10 \) \( \mu>10 \) \( \mu=10 \) \( x \quad \mu=10 \) COMPLETE What type of significance test should be used for this situation? DONE \( \square \) a left-tailed test a two-tailed test a right-tailed test

In this situation, the null hypothesis \( H_0 \) would be that the average number of fouls committed by the players is less than or equal to 10, which represents the coach's claim. Thus, \( H_0: \mu \leq 10 \) is the correct choice. The alternative hypothesis \( H_a \) will reflect the skepticism of the other coach, suggesting the average is more than 10, leading to \( H_a: \mu > 10 \). A right-tailed test is appropriate here as the alternative hypothesis is concerned with determining if the mean exceeds a specific value. Did you know that the concept of hypothesis testing in statistical analysis dates back to the early 20th century? Pioneers like Ronald Fisher helped lay the groundwork, creating methods that are essential for today's data analysis in fields ranging from psychology to sports! So, when you're evaluating those fouls, remember you're part of a long tradition of inquiry! If you're interested in diving deeper, consider exploring "The Art of Statistics: Learning from Data" by David Spiegelhalter. This fantastic read offers insights into the world of statistical thinking and its applications, perfect for those wanting to enhance their understanding of statistical methods in real-life scenarios. Plus, who knows, you might uncover how stats can make or break a team’s season!