Question

Testing the Difference Between Two Means: Dependent Samples

3.

D = Dn                       t = D-μDsD/√n

A physical education director claims by taking a special vitamin, a weight lifter can increase his strength. Eight athletes are selected and given a test of strength, using the standard bench press. After 2 weeks of regular training, supplemented with the vitamin, they are tested again. Test the effectiveness of the vitamin regiment at ∝ = 0.05

Athlete          1          2          3          4          5          6          7          8         

Before             210      230      182      205      262      253      219      216

After                219      236      179      204      270      250      222      216

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ(d) = 0
Alternative Hypothesis: μ(d) > 0

Test statistic,
t = (dbar - 0)/(s(d)/sqrt(n))
t = (2.38 - 0)/(4.8385/sqrt(8))
t = 1.391

P-value Approach
P-value = 0.1034
As P-value >= 0.05, fail to reject null hypothesis.