Question

A football coach claims that players can increase their strength by taking a certain supplement. To test the
theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The results are
listed below. Thirty days later, after regular training using the supplement, they are tested again. The new
results are listed below. Test the claim that the supplement is effective in increasing the athletesʹ strength.
Use α= 0.05. Assume that the distribution is normally distributed.

Use any method, however, follow the PHANTOMS acronym.

Athelete	1	2	3	4	5	6	7	8	9
Before	215	240	188	212	275	260	225	200	185
After	225	245	188	210	282	275	230	195	190

P - Parameter Statement

H - Hypotheses

A - Assumptions & Conditions

N - Name the Test and state the curve you're using

T - Test Statistic - Round your value to TWO decimals and state the command you used to find this value

O - Obtain the P-Value or Critical Value . State the command you are using to find these values

M - Make a Decision about the Null Hypothesis and explain why

S - State Your Conclusion About the Claim

Answer 1

Here, parameter = = average difference in the strength of the athletes before and after taking the supplement.
Now, for hypotheses, we have, (null hypothesis) versus (alternative hypothesis).
We assume that the underlying distribution is normally distributed. The distribution of the strength values does not contain any outlier. The strength values variable is continuous and the observations are independent of one another.
We will carry out a paired samples t-test and we will be using a bell-shaped curve.



Since the p-value is less than the 0.05 significance level, we reject the null hypothesis.
We conclude that there is enough evidence to support the claim that the supplement is effective in increasing the athletesʹ strength.