Question

A professional golfer wondered if she should switch to a new line of golf clubs that are supposed to put a spin on the golf ball that reduces the variance in the ball's flight. She obtained a new set of the clubs and paired off each new club with one of her old clubs. Then she hit golf balls with the pairs of clubs in 30 situations that would be appropriate to the type of club and measured how far the golf balls landed from her target. She tests the paired data, where α=0.10, in order to evaluate the claim that the true mean difference in distance is significantly greater than zero (determine if the new clubs perform better than the old clubs). (a) H0:μd=0; Ha:μd>0, which is a right-tailed test. Find T stat  and P value

Pair   Old Clubs   New Clubs
1   13   16
2   5   8
3   1   0
4   0   2
5   0   1
6   9   11
7   14   8
8   8   7
9   10   2
10   4   7
11   12   10
12   9   6
13   11   9
14   1   0
15   13   5
16   14   13
17   7   7
18   3   3
19   6   9
20   9   7
21   5   11
22   10   6
23   8   3
24   5   9
25   16   7
26   11   6
27   3   0
28   15   13
29   4   5
30   12   14

Answer 1

We have to perform paired t test.

So first we need to find differences d = Old clubs - New clubs

Then we can find the sample mean ( ) and standard deviation ( S_d ) of these differences using excel function =AVERAGE( ) and =STDEV.S() respectively

So = 1.1 and  S_d = 3.7815

H₀: μ_d=0 vs H_a : μ_d>0

t statistic :

t = =  

t = 1.59

To find p-value we can use excel function =TDIST( | t | , df , tail )

Here t = 1.59 , so | t | = 1.59 .  

df = n - 1 = 30 - 1 = 29

tail = 1 ( because one tail test )

=TDIST( 1.59 ,29 ,1 )

P-value = 0.0610