Problem 1

During the NBA seasons 1980-1982, when the Boston Celtics player Larry Bird shot a pair of free throws, he made both shots 251 times, he missed both shots 5 times, he made the first and missed the second 34 times, and he missed the first and made the second 48 times.

(a) Organize the data into a 2 by 2 table in R that cross tabulates the frequencies of made and missed shots for first shots versus second shots. Display the table in R.

(b) Calculate the estimated odds ratio and a 95% confidence interval for the odds ratio. Briefly interpret what the confidence interval says about association between first and second free throw shots.

(c) Calculate the expected 2 by 2 table under the independence hypothesis.

(d) Test for independence using Pearson's X² at level 0.10. What do you conclude?

(e) Display Pearson residuals for the table. Are the magnitudes of the residuals consistent with your conclusion in (d)? Explain why or why not.