Each day I am getting better in math A “subliminal”

message is below our threshold of awareness but may nonetheless influence us. Can subliminal messages help students learn math? A group of 18 students who had failed the mathematics part of the City University of New York Skills Assessment Test agreed to participate in a study to find out.

All received a daily subliminal message, flashed on a screen too rapidly to be consciously read.

The treatment group of 10 students (assigned at random) was exposed to “Each day I am getting better in math.” The control group of 8 students was exposed to a neutral message, “People are walking on the street.” All 18 students participated in a summer program designed to raise their math skills, and all took the assessment test again at the end of the program. The table below gives data on the subjects’ scores before and after the program.48 Treatment Group Control Group Pretest Posttest Difference Pretest Posttest Difference 18 24 6 18 29 11 18 25 7 24 29 5 21 33 12 20 24 4 18 29 11 18 26 8 18 33 15 24 38 14 20 36 16 22 27 5 23 34 11 15 22 7 23 36 13 19 31 12 21 34 13 17 27 10

(a) Explain why a two-sample t test is more appropriate than a paired t test for analyzing these data.

(b) The Fathom boxplots below display the differences in pretest and posttest scores for the students in the control (Cdiff) and treatment (Tdiff) groups. Write a few sentences comparing the performance of these two groups.

(c) Do the data provide convincing evidence that subliminal messages help students learn math?

(d) Can we generalize these results to the population of all students who failed the mathematics part of the City University of New York Skills Assessment Test? Why or why not?

Transcribed Image Text:

Tdiff Cdiff Subliminal messages 0 2 4 6 8 10 12 14 16 18 Box Plot