Statistical Reasoning in Sports

Statistical Reasoning in Sports Name: ______Chapter 3 Review

On April 25, 2010, basketball player Dwyane Wade of the Miami Heat scored 46 points in a playoff victory over the Boston Celtics. During the game many fans suggested that Wade had the hot hand. However, even though this was a truly amazing PERFORMANCE, it is possible that the outcomes of Wade’s shots were independent and he didn’t have the hot hand. Overall, he made 16 shots in 24 attempts. a) Explain what it means for the outcomes of Wade’s shots to be independent.

He has the same ability to make a shot after a made shot as he does after a missed shot. b) If we wanted to investigate if the Wade’s ABILITY to make a shot is greater following a made shot than following a missed shot, what hypotheses should we test?

H0: The outcomes of Wade’s shots are independent.

Ha: Wade is a streaky shooter.

c) Describe a Type I and a Type II error in the context of this problem.

A type 1 error would occur when we say that we have enough evidence to prove Wade is a streaky shooter when his shots are actually independent.

A type II error would occur if we determined that we do not have enough evidence to prove that wade is a streaky shooter when he actually is streaky. d) Suppose that a simulation was conducted assuming that Wade’s ABILITY to make a shot is the same after a made shot and after a missed shot and that the p-value was 15%. Interpret this value. This means that Wade’s performance or better occurred in 15% of our simulations. This would lead us to believe that his performance is likely to occur by random chance. e) Based on the p-value in part (e), are the results statistically significant? Explain.

No, the p-value is too large to be statistically significant. We cannot rule out random chance as the cause. f) Two other test statistics we can use to test these hypotheses are the length of the longest streak and the number of streaks of 3 or more. Underline each of the streaks in the list of outcomes below (Y = made shot and N = missed shot) and find the value of each of these test statistics.

NYNYYYYYNNYNYYNYYYYYYNYN

Longest streak: 6 Number of streaks of 3 or more: 2 g) Describe how to use index cards to simulate the distribution of both of these test statistics. We would need 24 cards, 16 labeled as Y and 8 labeled as N. Shuffle the cards and lay them out. Find and record the longest streak and the number of streaks of 3 or more. Repeat until you have enough simulations to reach a conclusion. h) 50 trials of a simulation were conducted assuming that the Wade’s ABILITY to make a shot is the same after a made shot and after a missed shot. The longest streak in each simulated game was recorded on the dotplot below. Based on these results, estimate the p-value.

p-value = 30/50 = 60%

2 4 6 8 10 LongestStreak i) Based on the p-value in question (i), what would be an appropriate conclusion? We do not have significant evidence to reject the null. Therefore, we cannot say that Wade was a streaky shooter. j) 50 trials of a simulation were conducted assuming that the Wade’s ABILITY to make a shot is the same after a made shot and after a missed shot. The number of streaks of at least 3 in a row in each simulated game was recorded on the dotplot below. Based on these results, estimate the p-value.

p-value = 50/50 = 100%

2 3 4 5 6 7 8 9 NumStreak3 k) Based on the p-value in question (k), what would be an appropriate conclusion? We do not have significant evidence to reject the null. Therefore, we cannot say that Wade was a streaky shooter.