Question

A researcher wants to evaluate the pain relief effectiveness of a new medication for chronic pain sufferers. Using a pain scale from 0 to 10 (where 0 = no pain at all, and 10 = the most pain you can imagine), she compares the pain level for a sample of n₁ = 4 people who received the new medication, with the pain level for a sample of n₂ = 4 people who received a placebo. The data are as follows:

Medication		Placebo
4		9
7		9
7		6
6		9

(a) Identify the Independent Variable (IV):

Pain level

People taking placebo   

People taking medication

Medication type

(b) Identify the Dependent Variable (DV):

Pain level

People taking placebo   

People taking medication

Medication type

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

μ₁ - μ₂ ≥ 0

μ₁ - μ₂ ≤ 0  

  μ₁ - μ₂ = 0

μ₁ - μ₂ ≠ 0

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

μ₁ - μ₂ > 0

μ₁ - μ₂ < 0  

  μ₁ - μ₂ = 0

μ₁ - μ₂ ≠ 0

(e) Compute df for an independent 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 Means for each group:

M₁ =
M₂ =

(h) Calculate the Sum of Squares (SS) for each group: (Use 3 decimal places.)

SS₁ =
SS₂ =

(i) Calculate the Pooled Variance: (Use 3 decimal places.)

S_P² =

(j) Calculate the Standard Error of the Difference in the Means: (Use 3 decimal places.)

S_(M1-M2) =

(k) Calculate the t statistic: (Use 3 decimal places.)

t =

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

Fail to reject the null hypothesis, there is not a significant difference between the placebo and medication groups.

Reject the null hypothesis, there is not a significant difference between the placebo and medication groups.  

  Reject the null hypothesis, there is a significant difference between the placebo and medication groups.

Fail to reject the null hypothesis, there is a significant difference between the placebo and medication groups.

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

d =
r² =

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

The participants taking the pain medication reported less pain (M = 6, SD = 1.414) than the participants taking the placebo (M = 8.25, SD = 1.500). This difference was not significant, t(6) = -2.183, p > 0.05.

The participants taking the pain medication reported less pain (M = 6, SD = 1.414) than the participants taking the placebo (M = 8.25, SD = 1.500). This difference was significant, t(7) = -2.183, p < 0.05.    

The participants taking the pain medication reported less pain (M = 6, SD = 1.414) than the participants taking the placebo (M = 8.25, SD = 1.500). This difference was significant, t(6) = -2.183, p < 0.05.

The participants taking the pain medication reported less pain (M = 6, SD = 1.414) than the participants taking the placebo (M = 8.25, SD = 1.500). This difference was not significant, t(7) = -2.183, p > 0.05.

Answer 1