Is a basketball player’s ability to make free throws different when they get their own rebound or when someone else gets their rebound for them? This is what student researchers wanted to explore. The researchers used students (20 females and 20 males) taking a college physical education class as their subjects. The students each attempted 10 shots from the free throw line where they had to get their own rebound and 10 shots where someone else got their rebound and passed the ball back to them while they stayed on the free throw line. They randomly determined the order that they took these shots, with some getting their own rebounds first and some having someone else get the rebounds first. Here are the hypotheses. 

H₀: There is no association between how the ball is rebounded and the number of shots made (μ_d = 0). 

H_a: There is an association between how the ball is rebounded and the number of shots made (μ_d ≠ 0). The students found the following results for the number of baskets made.

a. What are the explanatory and response variables in this study and what types of variables are they (categorical or quantitative)? 

b. Is this an observational study or a randomized experiment? 

c. What is the observed statistic for this study? 

d. Assuming a true null hypothesis, we simulated this study and found 5,000 mean differences that are shown in the null distribution in the Exercise 7.2.16d output. Based on where the observed statistic lies in the distribution, does the p-value appear to be very small? 

e. What is the standardized statistic for this test? 

f. Based on the standardized statistic from part (e), is there strong evidence that number of shots made differs between rebounding methods, on average? Explain.  

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Mean Standard deviation Rebounded Self-rebounded 3.875 3.000 2.399 2.320 Difference 0.875 1.977