Chapter 9.3, Problem 98E

To determine

To Explain: that this result is statistically significant, but not practically important.

Answer to Problem 98E

P-value is small and therefore the result is statically. Improvement of 0.08 seconds is small and therefore the result is not practically important.

Explanation of Solution

Given:

  $\begin{array}{l}{H}_0:\mu =40\\ H_1:\mu <40\\ \overline{x}=39.92\\ P-\text{value=0}\text{.0002}\end{array}$

Assume that the significance level $\alpha$ is 0.05.

  $\alpha =0.05$

If the P-value is less than the significance level, then reject the null hypothesis $H_0$ and then the result is statically significant.

  $\text{0}\text{.0002}<0.05\Rightarrow \text{Statistically significant}$

It is observed that the result is statically significant.

However, the result is not practically important, the reason is that the improvement was only by 40-39.92=0.08 seconds and these 0.08 seconds are not a very big improvement in the completion time of the maze.