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? \( \mu<10 \) \( \mu \leq 10 \) \( \mu>10 \) \( \mu \geq 10 \) DONE

In hypothesis testing, the null hypothesis (\( H_{0} \)) represents a statement of no effect or no difference, and it is what we seek to test against. In this case, the basketball coach claims that the team's players commit, on average, no more than 10 fouls per game. The alternative hypothesis (\( H_{a} \)) is what the other coach believes, which is that the players create more fouls than the claimed average. Given this context, the null hypothesis should reflect the coach's claim that the average number of fouls is at most 10. Therefore, the correct null hypothesis is: \[ H_{0}: \mu \leq 10 \] This means that the average number of fouls per game is less than or equal to 10, which aligns with the coach's assertion. The other options do not accurately represent the null hypothesis in this context: - \( \mu < 10 \) suggests that the average is strictly less than 10, which is not what the coach claims. - \( \mu > 10 \) and \( \mu \geq 10 \) represent the alternative hypothesis or incorrect null hypotheses. Thus, the correct answer is: \[ H_{0}: \mu \leq 10 \]