Reaction times Catherine and Ana wanted to know if student-athletes (students on at least one varsity team) have faster reaction times than non-athletes. They took separate random samples of 33 athletes and 30 non-athletes from their school and tested their reaction time using an online reaction test, which measured the time (in seconds) between when a green

light went on and the subject pressed a key on the computer keyboard. A 95% confidence interval for the difference (Non-athlete − Athlete) in the mean reaction time was$\frac{305}{1526}=0.200=20.0\%0.018\pm 0.034$seconds

a. Does the interval provide convincing evidence of a difference in the true mean reaction time of athletes and non-athletes? Explain your answer.

b. Does the interval provide convincing evidence that the true mean reaction time of athletes and non-athletes is the same? Explain your answer.

The$95\%$confidence interval for the difference in mean reaction time between athletes and non-athletes is as follows:

role="math" localid="1654714398940" $$\begin{gathered} 0.018\pm 0.034=(0.018-0.034,0.018+0.034) \\ =(-0.016,0.052) \end{gathered}$$

Then we notice that the confidence interval contains zero, implying that the difference in mean reaction time is likely to be zero, implying that there is no difference.

This means that there is no convincing evidence that athletes and non-athletes have different true mean reaction times.

The $95\%$confidence interval for the difference in mean reaction time between athletes and non-athletes is as follows:

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

Then we notice that the confidence interval contains zero, implying that the difference in mean reaction time is likely to be zero, and thus that no difference exists.

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