Chapter 12.5, Problem 65E

Torsion during hip external rotation and extension may explain why acetabular labral tears occur in professional athletes. The article “Hip Rotational Velocities During the Full Golf Swing” (J. of Sports Science and Med., 2009: 296–299) reported on an investigation in which lead hip internal peak rotational velocity (x) and trailing hip peak external rotational velocity (y) were determined for a sample of 15 golfers. Data provided by the article’s authors was used to calculate the following summary quantities:

$\begin{array}{l}\sum {(x_i-\bar{x})}^2=64,732.83,\sum {(y_i-\bar{y})}^2=130,566.96,\\ \sum (x_i-\bar{x})(y_i-\bar{y})=44,185.87\end{array}$

Separate normal probability plots showed very substantial linear patterns.

1. a. Calculate a point estimate for the population correlation coefficient.
2. b. Carry out a test at significance level .01 to decide whether there is a linear relationship between the two velocities in the sampled population.
3. c. Would the conclusion of (b) have changed if you had tested appropriate hypotheses to decide whether there is a positive linear association in the population? What if a significance level of .05 rather than .01 had been used?