A researcher believes she has developed a new medicine that can reduce anxiety among American adults. To test her hypothesis, the researcher takes a random sample of 8 American adults and conducts a repeated measures experiment. She measures the self-reported anxiety levels of the same 8 adults before and after they are given the experimental anxiety medicine.

The sample data are given below:

person anxiety score before medicine anxiety score after medicine difference (after medicine-before medicine)
1 52 50 -2
2 49 46 -3
3 54 54 0
4 56 52 -4
5 43 44 1
6 60 59 -1
7 54 50 -4
8 58 54 -4
a) The researcher will do a one-tailed, related-samples t test. What are the correct null and alternative hypotheses? (stated in either words or symbolic notation)

b) What are the degrees of freedom?

c) What is the critical value of t with alpha = 0.05?

d) What is the sample mean difference, (Mdifference)?

e) What is the sample standard deviation of the differences, (s)?

f) What is the standard error of the sample mean difference?

g) What is the t statistic?

h) Do you reject or fail to reject the null hypothesis?

i) Interpret your decision from (h).

j) Estimate Cohen’s d.

k) Provide a brief interpretation of Cohen’s d.