Data set: Tennis
Students on the college tennis team were interested in knowing if string tension affected the speed and accuracy of a tennis ball. They had recently read an article in the Journal of Sports Sciences and decided conduct a similar study for themselves. After warming up, five men’s varsity tennis players volunteered to hit 30 serves using three different racquet tensions over three days. Day was not treated as a factor of interest in the study, but used to avoid fatigue in the players. For each serve, players aimed at a target in the back center of the service box, and accuracy was measured as the distance in inches from the center of the box to the ball strike location. A radar gun was used to measure the velocity of each player’s serve. Use Speed as the response variable for each of the following questions:
a. Write the null and alternative hypotheses corresponding to the original research questions.
b. To avoid bias, all players used a Wilson K Factor KSix-One Tour 90 racquet (which has a recommended string tension of between 50 and 60 pounds).* In addition, each player used new balls each day and racquets were restrung after each day. Identify any questions or concerns you have about potential sources of bias in this study.
c. Use software to conduct an ANOVA to analyze the Tennis data set using a block design.
d. Create a main effects plot comparing the effects of Player and Racquet. Explain how the p-values correspond to what you see in the main effects plot.
e. The goals of this study did not include determining if there was a difference between the performance of Players. Based on the degrees of freedom, sum of squares, and p- value for Player provided in the ANOVA, do you believe that blocking was helpful in this study?
f. Create a probability plot or histogram of the residuals to determine if the residuals are consistent with data from a normal distribution.
g. State your conclusions for this study. Be sure to clearly identify the population for which these conclusions hold and also state whether causation has been shown.