Impact of dropping ping-pong balls. Refer to theAmerican Journal of Physics (Mar. 2014) study of the impact of dropping ping-pong balls, Exercise 11.122

(p. 666).

Recall that 19 standard ping-pong balls were dropped vertically onto a force plate. The data on y = coefficient of restitution (COR, measured as a ratio of the speed at impact and rebound speed), x1 = speed at impact

(meters/second), and x2 = 51 if ball buckled, 0 if not6 are reproduced in the table on p. 741. Consider the interaction model E1y2 = b0 + b1x1 + b2x2 + b3x1x2.

A MINITAB print out of the regression analysis is also shown on p. 741.

a. Give the equation of the hypothesized line relating COR (y) to impact speed (x1) for ping-pong balls that did not buckle. What is the estimated slope of this line?

b. Repeat part a for ping-pong balls that buckled.

c. The researcher believes that the rate of increase in COR with impact speed differs depending on whether the ping-pong ball buckles. Do the data support this hypothesis?
Conduct the appropriate test using a = .05.

Transcribed Image Text:

Data for Exercise 12.106 COR SPEED BUCKLE Ball y X1 X2 123456789: .945 0.8 0 (No) .950 1.0 0 (No) .930 1.5 0 (No) .920 1.8 0 (No) .920 3.0 0 (No) .930 3.4 0 (No) .905 4.4 0 (No) .915 5.0 0 (No) .910 6.4 0 (No) 10 .900 4.4 1 (Yes) 11 .885 5.3 1 (Yes) .870 5.4 1 (Yes) .850 7.4 1 (Yes) 14 .795 7.2 1 (Yes) 15 .790 7.2 1 (Yes) 17 18 19 6989 16 .800 8.0 1 (Yes) .820 8.5 1 (Yes) .810 9.4 1 (Yes) .780 9.0 1 (Yes)