Chapter 10.2, Problem 49E

(a)

To determine

To explain does the interval provide convincing evidence of a difference in the true mean reaction time of athletes and non-athletes or not.

Answer to Problem 49E

No.

Explanation of Solution

The $95\%$ confidence interval for the difference in the mean reaction time of athletes and non-athletes:

  $\begin{array}{l}0.018\pm 0.034=(0.018-0.034,0.018+0.034)\\ =(-0.016,0.052)\end{array}$

Then we note that the confidence interval contains zero which implies that it is likely that the difference in the mean reaction time is zero and thus likely that there is no difference.

This implies that there is no convincing evidence of a difference in the true mean reaction time of athletes and non-athletes.

(b)

To determine

To explain does the interval provide convincing evidence that the true mean reaction time of athletes and non-athletes is the same or not.

Answer to Problem 49E

No.

Explanation of Solution

The $95\%$ confidence interval for the difference in the mean reaction time of athletes and non-athletes:

  $\begin{array}{l}0.018\pm 0.034=(0.018-0.034,0.018+0.034)\\ =(-0.016,0.052)\end{array}$

Then we note that the confidence interval contains zero which implies that it is likely that the difference in the mean reaction time is zero and thus likely that there is no difference.

However, there is no evidence that the true mean reaction time of athletes and non-athletes is the same because the difference of zero is one of the plausible values but there are many other plausible values in the confidence interval for the difference.