Question

Pre-service routines in tennis. Successful athletes often engage in a particular routine before attempting some element of their sports; doing so may improve performance (e.g., before attempting a free throw, a basketball player may rub her chin on her left shoulder and bounce the ball twice). Rob West, a CSU tennis player who graduated in 2009, investigated whether preservice routines would improve the performance of novice tennis players. Players were assigned at random to one of four groups—an arousal-adjustment group, an imagery group, a combination group (which was taught both the arousal-adjustment and imagery techniques), and a control group. There were 10 participants in each group. In a pretest, each participant attempted 20 serves into a target box drawn on the court; and was given instructions about the pre-service routine for the condition to which he or she had been assigned and told to use that routine every time he or she served a tennis ball. Two weeks later, each participant again attempted 20 serves into the target box. Rob was interested in differences among the four conditions in performance improvement, but for this question, you are only to determine whether there was statistically significant performance improvement between the pretest and the posttest in the condition you are assigned to analyze. The data are in the following table; in each condition, a particular participant’s scores (number of successful serves in the pretest and in the posttest) are shown on one row.

Control

pretest posttest
8 6
6 7
10 10
7 5
5 5
6 7
4 3
3 5
7 5
5 4
For the condition assigned to you, do the data provide good evidence (α = .01) that practicing the assigned preservice routine improved performance? In answering the following, remember that you are analyzing matched-pairs data, because each participant provided a pretest score and a posttest score. a) State null and alternative hypotheses, identifying the µ used in these hypotheses.

b) For the data assigned to you, (i) calculate a t statistic, (ii) give its degrees of freedom, and (iii) find its P-value, indicating whether the P-value is one-sided or two-sided. (Be sure to do each of these three things.) (To do this, you will need the mean and standard deviation of the pretest-postest differences for your condition.)

c) With α = .01, say whether the data provide good evidence that in the condition that you are analyzing, learning the assigned preservice routine was effective at improving serving performance.

Answer 1

Check the explanation

Explanation:

a)

Null Hypothesis Alternate Hypothesis

H0: μ1 - μ2 = 0 Ha: μ1 - μ2 < 0

b)

dbar = μ(before) - μ(after) 0.4

s(dbar) 1.4298

SE = s(dbar)/sqrt(n) 0.4522

Test Statisitcs, t = dbar/SE 0.8847

degrees of freedom = n-1 9

p-value 0.199680679522717

c)

As p-value is greater than the significance level of 0.01, we fail to reject the null hypothesis

this means there are not sufficient evidence to conclude that learning the assigned preservice routine was effective at improving serving performance