Question

3. A researcher is interested in brain training services like Luminosity affects the speed with which people can solve puzzles. To test this, she has research participants complete brain training exercises daily, and measures the speed with which they solve a puzzle at four different times: before practice, after 1 week of training, after 2 weeks of training, and after 3 weeks of training. Eight subjects participate in the experiment; each subject receives every level of the IV. Their data (time in minutes needed to solve the puzzle) are given below:

	Factor A: Practice
Participant	No training	1 week	2 weeks	3 weeks
1	32	28	27	28
2	24	23	20	19
3	20	21	18	12
4	21	19	19	17
5	25	20	23	21
6	26	25	20	22
7	17	21	17	14
8	24	23	19	20
9	26	24	18	15
10	23	26	22	22
11	21	20	18	16
12	20	20	16	15

1. Compute an ANOVA to evaluate whether brain training has an effect on the speed of solving puzzles. Complete the ANOVA summary table. (6 points)

2. Using  = .05, what do you conclude about the effects of Luminosity? Be sure to include a discussion of the critical value in your answer (1.5 points).

Answer 1

(a)

Hypothesis:

H₀ : The brain training has no effect on the speed of solving puzzles.

H1 : The brain training has an effect on the speed of solving puzzles.

(b) The value of F-test statistics = 4.7802

The critical value of F = 2.8165

Conclusion: The value of F test statistic is greater than the critical value of F. Hence we reject null hypothesis at 0.05 significance level and conclude that the brain training like Luminosity has an effect on the speed of solving puzzles.