A coach is examining two basketball players’ free-throw percentages over the last few games. Bob made 34 out of 85 shots and Joe made 72 out of 125 shots. The coach wants to know if Bob is a 10% worse free-throw shooter than Joe. Which of the following would be the p-value of the corresponding test?Multiple Choice0.27280.13640.45440.4322

To answer this question, we first need to calculate the free-throw percentages for both Bob and Joe.

1. Calculate Bob's free-throw percentage: Bob made 34 out of 85 shots. So, his free-throw percentage is (34/85)*100 = 40%.

2. Calculate Joe's free-throw percentage: Joe made 72 out of 125 shots. So, his free-throw percentage is (72/125)*100 = 57.6%.

The coach wants to know if Bob is a 10% worse free-throw shooter than Joe. This means we need to check if Bob's free-throw percentage is 10% less than Joe's.

3. Calculate 10% of Joe's free-throw percentage: 10% of 57.6 is 5.76.

4. Subtract this 10% from Joe's percentage to find the value Bob's percentage would be if it was 10% worse: 57.6 - 5.76 = 51.84%.

Bob's actual free-throw percentage is 40%, which is more than 10% worse than Joe's.

However, the question asks for the p-value of the corresponding test. The p-value is a statistical measure that helps scientists determine whether their hypotheses are correct. Typically, if the p-value is less than 0.05, then the null hypothesis is rejected.

In this case, the null hypothesis would be that Bob is not a 10% worse free-throw shooter than Joe. To calculate the p-value, we would need to perform a statistical test, such as a t-test or a z-test.

Unfortunately, without more information or the ability to perform these tests, we cannot determine the p-value. The options provided (0.2728, 0.1364, 0.4544, 0.4322) are likely results from a statistical test, but without knowing the test or having the data to perform it, we cannot definitively choose one.