Question

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 10 months, their vertical jump heights are measured again. The vertical jump heights (in inches) for each athlete and some statistics are given in the table below. Athlete 1 2 3 4 5 6 7 8 Mean SD jump height before using the shoes 32 26 23 28/34 2821 29 27.6250 4.3074 jump height after using the shoes 35 30 23 29 31 29 24 32 29.1250 3.9799 difference 3 4 0 1 -3 1 3 3 1.5000 2.2678

Where difference = jump height after shoes − jump height before shoes. At α = 0.10, is there enough evidence to support the manufacurer’s claim? Assume the vertical jump heights are normally distributed.

1 . Null hypothesis, μd = μafter − μbefore

2. Alternative hypothesis, μd = μafter − μbefore

3. which of the following is the appropriate test for these data?

a) paired t test

b) two - independent samples Z test

c) two samples t test

d) two- independent samples t test

4. observed test statistic

5. the degrees of freedom for the test statistic

6. p - value

7. Would you support the manufacturer’s claim at 5% significance level?

a) yes

b) no

c) not enough information to decide

Answer 1

it Null hypothesis ! Ho! Md = 0 Vs Hi Mayo 2) Alternative hypothesis: Hii Hd > 0 3) test for paired- t will is appropriate these data. 4 Test statistic : - to-l tral= $d 180 where a = e di 2.2678 165 S d = 2.2678 n=8 1.5 tcals 2.2648/58 0:3018 teal ho It col 1.870829 57 Degrees of freedom: n-1 = 7 6) Pvalue = P(Ty teal) = 0.05177 Decision Puabe La (2=0.10) Conclusion Reject Ho at 10 % L.O.S. le There is evidence to all support manufactures claim at 10% L.O.S. 7 pvole ya (0.05) Accept Ho at 5% L.O.S. NO, I would not support manufacturer's claim at 5 % LOS