Question

The researchers tested performance on a task before and after training on a video-game task. 20 non-gamers participate in the study. There is a mean improvement of 24 ms. in reaction time on the task , with a variance of 18.

1. Calculate the t-statistic. SHOW YOUR WORK.

2. Use the table on page 243. Is the result is statistically significant?

3. Report the results in a sentence, using APA style.

Answer 1

Let d denotes the difference in reaction time between before  and after training on a video-game task.

To test against

Here

sample mean of difference

sample variance

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 5% level of significance if

Now,

The value of the test statistic

and critical value

Since , so we reject H₀ at 5% level of significance and we can conclude that the result is significant,i.e. there is significant difference in reaction time between before  and after training on a video-game task.