An article titled ?TCU Horned Frogs Game Preview (Part 1)? (uwdawgpound.com/2016/11 /26/13710900/washington-huskies-tcu-horned -frogs-game-preview-part-1, retrieved December 20, 2016)

Question:

An article titled ?TCU Horned Frogs Game Preview (Part 1)? (uwdawgpound.com/2016/11 /26/13710900/washington-huskies-tcu-horned -frogs-game-preview-part-1, retrieved December 20, 2016) previews a college basketball game between the University of Washington Huskies and the TCU Horned Frogs. The profile for TCU player Kenrich Williams states, ?He has the statistical oddity of shooting better from behind the arc than from the free throw line but that?s a marker of small sample sizes.? (Note that ?behind the arc? means three-point shots, which are taken behind an arc relatively far from the basket.) At that point in the season, TCU had played five games. Kenrich Williams had made 4 of the 10 free throws that he had attempted (40%), and 3 of the 7 three-point shots that he had attempted (42.9%).

Suppose that it is reasonable to consider these shots to be representative sample of Williams?s abilities to make free throws and three-point shots for the 2016?2017 college basketball season.

a. Explain why the data in this exercise should not be analyzed using a large-sample hypothesis test for the difference in two population proportions.

b. Use the output at the top of the next page from the Shiny app ?Randomization Test for Two Proportions? to carry out a hypothesis test to determine if there is evidence that supports the statement that Williams is a better shooter from behind the arc than from the free throw line.

c. Use the output to identify a 95% confidence interval for the difference in the proportions of made free throws and made three-point shots by Kenrich Williams for the 2016?2017 season. Interpret the confidence interval in context.