Chapter 27, Problem 39E

To determine

To test an appropriate hypothesis.

Explanation of Solution

Given:

  

The null and alternative hypotheses:

  $\begin{array}{l}{H}_0:{\beta }_1=0\\ H_a:{\beta }_1\ne 0\end{array}$

Using excel,

  

Test statistic:

t = -4.34

P-value = 0.0004

Decision: P-value < 0.05, reject H₀.

Conclusion: There is sufficient evidence that the slope is non zero and strong evidence that the effectiveness of the video depends on the player’s initial ability. As slope is negative, it can be say that those who were above average initially tended to be worse after training. And those who were below average initially tended to improve after training.