Question

How can I apply the data that is in the box to these questions? Specifically, part F. Thanks!

1. Some tennis players make audible noises when producing their groundstrokes (i.e., forehand, backhand), often quite loudly. For example, some of Maria Sharapova’s grunts have been measured at over 100 decibels (roughly as loud as a lawnmower or motorcycle). Given the loudness of these grunts, some have accused “grunters” of cheating by distracting their opponents. But are grunts actually distracting? Sinnett and Kingstone (2010) attempted to answer this question. In their study, participants were presented with videos of a tennis player hitting a ball to either side of a tennis court. For half of the participants, grunts were digitally added to the video at the point that the tennis player made contact with the ball, and for half of the participants, no grunts were added to the video. The participants’ task was to respond as quickly as possible, indicating whether the ball was being hit to the left- or right-hand side of the court. Below are the summary statistics of the study, with mean response times (i.e., time required to make a decision as to the trajectory of the ball) and standard deviations for both the grunt group and the no grunt group. The researchers reasoned that if grunting negatively impacts the opponent’s ability to judge the trajectory of the ball, then response times should be longer for the grunt group than for the no grunt group. Do the data support their hypothesis?

Grunt	No grunt
m=490 ms	M=483ms
SS=3100	SS=2511
N=32	N=32

1. What is the null hypothesis?

2. What is the research hypothesis?

3. What is the critical value of your test statistic? Be sure to specify df.

4. What is the obtained value of your test statistic?

-First, calculate the pooled variance.

Note: the sum of squares for each sample has already been calculated and is provided in the data box above (for the grunt sample, SS = 3100, and for the no grunt sample, SS = 2511)

-Second, calculate the t-statistic.

5. What is your statistical conclusion?

Answer 1

Given that,
mean(x)=490
standard deviation , s.d1=10
number(n1)=32
y(mean)=483
standard deviation, s.d2 =9
number(n2)=32
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.67
since our test is right-tailed
reject Ho, if to > 1.67
calculate pooled variance s^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
s^2 = (31*100 + 31*81) / (64- 2 )
s^2 = 90.5
we use test statistic (t) = (x-y)/sqrt(s^2(1/n1+1/n2))
to=490-483/sqrt((90.5( 1 /32+ 1/32 ))
to=7/2.378
to=2.943
| to | =2.943
critical value
the value of |t α| with (n1+n2-2) i.e 62 d.f is 1.67
we got |to| = 2.943 & | t α | = 1.67
make decision
hence value of | to | > | t α| and here we reject Ho
p-value: right tail -ha : ( p > 2.9433 ) = 0.00228
hence value of p0.05 > 0.00228,here we reject Ho
ANSWERS
---------------
a.
null, Ho: u1 = u2
alternate, H1: u1 > u2
b.
T test for difference of means with equal variance
d.
test statistic: 2.943
c.
critical value: 1.67
e.
pooled variance = 90.5
decision: reject Ho
p-value: 0.00228
f.
we have enough evidence to support the claim that if grunting negatively impacts the opponent’s ability to judge the trajectory of the ball, then response times should be longer for the grunt group than for the no grunt group.