After years of development, the FDA has approved human testing for a new depression treatment called esketamine. While other labs have started studies comparing to multiple existing treatment options, one lab is interested in the effect of esketamine on those who have treatment-resistant depression. This lab recruits 10 people with treatment-resistant depression and randomly assigns them into two groups: a "treatment-as-usual" group (control) and an esketamine group (treatment). After 6 weeks of treatment, you have the participants complete a depression survey. The depression scores (lower scores mean less depression) are shown below. The researchers have not hypothesized that esketamine will show an improvement, they are looking to see if there is only a difference.

Treatment as usual group:	Esketamine group:
5	6
6	6
2	4
8	5
5	3

1. State the null and alternative hypothesis for the study above, include the mathematical notation for each.

1. Calculate the following for the study above (show your work):
   1. Mean

1. Sum of Squares

1. Degrees of freedom and Variance

1. Standard error

1. t statistic

1. Assuming an alpha of .05, use the t-distribution table in the back of your textbook (p. 651) and find the critical value for your test. Are the results for the t-test significant? What decision can you make in regards to the null hypothesis?

1. Using the example study above, how would you change the study to conduct a repeated measures design? List at least two benefits of doing a repeated measures design.