Question

Pro sports shoes are name brand shoes that advertise improved jumping abilities for the show wearer. 6 participants are selected to test this claim. Each participant is given a pair of the same off brand shoes (in their size) and their jump height is measured. Each participant then changes into pro sports shoes and a new jump height is measured. The results of the tests are shown below.

Player	Off brand	Pro sports
1	4.8	7.1
2	6.1	5.7
3	3.9	7.2
4	5	6.9
5	5.1	6.5
6	5.2	4.8

Can it be concluded that wearing pro sports shoes improves jump height? Use the appropriate hypothesis test with α=0.05. assume the differences are normally distributed

Answer 1

The null and alternative hypotheses are: Ho: ud = 0 H: Md 70 The test statistic is: t=-2.216 The p-value = 0.039 Conclusion: The p-value of t test is less than 0.05. Hence we reject null hypothesis at 5% level of significance and conclude that wearing pro sports shoes improves jump height.

t-Test: Paired Two Sample for Means Off brand 5.017 Pro sports 6.367 Mean 0.502 0.887 6 Variance Observations Pearson Correlation Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 6 -0.629 0 5 -2.216 0.039 2.015 0.078 2.571