Question

A “subliminal” message is below our threshold of awareness but may nonetheless influence us. A study looked at the effect of subliminal messages on math skills. Messages were flashed on a screen too rapidly to be consciously read. Twenty-eight students who had failed the mathematics part of the City University of New York Skills Assessment Test were randomly assigned to receive daily either a positive subliminal message (“Each day I am getting better in math”) or a neutral subliminal message (“People are walking on the street”). All students took the assessment test again at the end of the program, and the table below gives the data on each of the subjects’ scores before and after the program. Is there statistical evidence that the positive message brought about a greater improvement in math scores than the neutral message? Make no assumptions and show all work.

	Positive Message
Before	After	Difference
18	24	6
18	25	7
21	33	12
18	29	11
18	33	15
20	36	16
23	34	11
23	36	13
21	34	13
17	27	10

	Neutral Message
Before	After	Difference
18	29	11
24	29	5
20	24	4
18	26	8
24	38	14
22	27	5
15	22	7
19	31	12

Ho:
Ha:
Exact P for F test:
test-statistic:
df:
Exact P value for the test-statistic
Conclusion relative to the hypothesis:
	ts= , df= ,P=

Got the data by Excel

Answer 1

Using Levene's test, we get

The value of test statistic = 0.42

and P-value = 0.526

Since P-value > 0.05, so we fail to reject H₀ at 5% level of significance and we can conclude that the two variances are not significantly different.

Now, assuming two distributions have equal variances, we need to perform a two sample t test with equal but unknown variances to test the means.

Let denote mean difference in math scores in positive message and neutral message respectively.

Conclusion : There is strong statistical evidence that the positive message brought about a greater improvement in math scores than the neutral message