Question 2a: An energy drink marketer hypothesizes that drinking their energy drink can improve student’s grades. A sample of n = 4 students completed a set of math problems from the SAT and their performance is measured. These 4 students then drink an energy drink and were given the exact same list of SAT problems to complete again. The number of correct solutions each student made before and after drinking the energy drink are listed below.  The marketing researcher claims that if the drink has no effect on test performance and the null is true, the expected difference between the groups would be μ-difference = 0.

Using the appropriate t test, with alpha set to .05, find whether drinking the energy drink had a significant effect on increasing test performance.

1. Report sample value:

2. Report T critical value(s):

3. Write a one sentence conclusion of your test:

4. Find the cohen’s d effect size value for this study. Report it and whether it is large, medium, or small.

5. Suggest a change to the study design, type of analysis used, or hypothetical values the researchers propose that could improve this study.