Question

Researchers wants to know if taking the herbal supplement St. John's Wort will affect depression. First, they measure the depression level of a sample of n = 4 depressed people (Pre-Test Scores). Then after a week of taking St. John's Wort, they again measure the sample's depression levels (Post-Test Scores). Note that high scores on the depression measure indicate more depression, whereas low scores indicate less depression.

Participant	Pre-Test Scores	Post-Test Scores
A	8	6
B	11	4
C	10	6
D	13	6

(a) Identify the Independent Variable (IV):

-Depression level

-People taking not taking St. John's Wort

- People taking St. John's Wort

-St. John's Wort

(b) Identify the Dependent Variable (DV):

-Depression level

-People taking not taking St. John's Wort  

- People taking St. John's Wort

-St. John's Wort

(c) What is the null hypothesis (H₀) for a two-tailed test?

a) μ_D ≥ 0

b) μ_D ≤ 0

c) μ_D = 0

d) μ_D ≠ 0

(d) What is the alternative hypothesis (H₁) for a two-tailed test?

a) μ_D ≥ 0

b) μ_D ≤ 0  

c)  μ_D = 0

d) μ_D ≠ 0

(e) Compute df for the related samples t test.

df =

(f) Use the t distribution table in Appendix B to determine the critical value of t for a two-tailed test at the 0.05 level of significance. (Use 3 decimal places.)

t-critical = ±

(g) Calculate the difference scores and M_D.

Participant	Pre-Test Scores	Post-Test Scores	D	D2
A	8	6
B	11	4
C	10	6
D	13	6
			ΣD =	ΣD2 =

M_D =

(h) Compute the Sum of Squares, sample variance, and estimated standard error for the difference scores (D).

SSD =	(Use 3 decimal places.)
s2D =	(Use 3 decimal places.)
sMD =	(Use 3 decimal places.)

(i) Compute the t-statistic for your data. (Use 3 decimal places.)

t =

(j) What decision should be made about the null hypopthesis (H_o)?

a) Fail to reject the null hypothesis, there is no significant reduction in depression.

b) Reject the null hypothesis, there is no significant reduction in depression.    

c) Reject the null hypothesis, there is a significant reduction in depression

d) Fail to reject the null hypothesis, there is a significant reduction in depression.

(k) Calculate the estimated Cohen's d and r² to measure effect size for this study. (Use 3 decimal places.)

d =
r² =

(l) How would the results be presented in the literature?

a) Taking St. John's Wort reduced depression levels by an average of (M = -5, SD = 2.449). This treatment effect was not significant, t(4) = -4.082, p > 0.05.

b) Taking St. John's Wort reduced depression levels by an average of (M = -5, SD = 2.449). This treatment effect was not significant, t(3) = -4.082, p > 0.05.   

c) Taking St. John's Wort reduced depression levels by an average of (M = -5, SD = 2.449). This treatment effect was significant, t(3) = -4.082, p < 0.05.

d) Taking St. John's Wort reduced depression levels by an average of (M = -5, SD = 2.449). This treatment effect was significant, t(4) = -4.082, p < 0.05.

Answer 1