Question 1178999: Example 1: A shoe manufacturer claims that athletes can increase their vertical jump heights using the manufacturer's training shoes. The vertical jump heights of eight randomly selected athletes are measured. After the athletes have used the shoes for 8 months, their vertical jump heights are measured again. The vertical jump heights (in inches) for each athlete are shown in the table. At α=0.10, is there enough evidence to support the manufacturer's claim? Assume the vertical jump heights are normally distributed.
Athlete
1
2
3
4
5
6
7
8
Vertical jump height (before using shoes)
24
22
25
28
35
32
30
27
Vertical jump height (after using shoes)
27
29
26
31
30
37
39
32
Conditions:
Significance Level:
Hypothesis:
Conclusion:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! This is a two sample t test.
Assume normally distributed, and that sigma may be approximated by s. Each athlete is his or her own control.
Ho: difference=0
Ha: difference NE 0
alpha 0.10 p{reject Ho|Ho true}
test paired t 0.95, df=7
critical value |t|>1.895
test is t=(d-0)/s/sqrt(8)
mean is 3.5
s=4.24
t=3.5*sqrt(8)/4.24=2.33
reject Ho
there is evidence to support a difference in favor of the new shoes.
p-value is 0.026
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