10. Head movement evaluations are important be cause individuals, especially those who are dis abled, may be able to operate communications aids in this manner. The article "Constancy of Head Turning Recorded in Healthy Young Humans" (J. of Biomed. Engr., 2008: 428-436) reported data on ranges in maximum inclination angles of the head in the clockwise anterior, pos terior, right, and left directions for 14 randomly selected subjects. Consider the accompanying data on average anterior maximum inclination angle (AMIA) in both the clockwise (Cl) and counterclockwise (Co) directions.

Subj: 1 2 3 4 5 6 7 Cl: 57.9 35.7 54.5 56.8 51.1 70.8 77.3 Co: 44.2 52.1 60.2 52.7 47.2 65.6 71.4 Subj: 8 9 10 11 12 13 14 Cl: 51.6 54.7 63.6 59.2 59.2 55.8 38.5 Co: 48.8 53.1 66.3 59.8 47.5 64.5 34.5 a. Construct boxplots of both the clockwise and counterclockwise direction observations, and comment on any interesting features. b. Construct a scatterplot of the data. What does it suggest about the general nature of the relation ship between Cl and Co? c. Calculate the value of the sample correlation coefficient. Does it confirm your impression from the scatterplot?

11. Torsion during external rotation and extension of the hip may explain why acetabular labral tears occur in professional athletes. The article "Hip Rotational Velocities During the Full Golf Swing" (J. of Sports Sci. 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 cal culate the following summary quantities: ^(xi 2 x) 2 5 64,732.83, ^(yi 2 y) 2 5 130,566.96, ^(xi 2 x)(yi 2 y) 5 44,185.87 Based on this, compute the sample correlation coefficient and interpret its value. How would you characterize this correlationas strong, moderate, or weak?