Question

1. A researcher developed a painkiller and wanted to test its effect. He recruited a group of 20 people who suffer from chronic pain of a similar level. Among these 20 participants, 10 participants received the painkiller and the other 10 participants received a placebo. One hour after taking the pills, the participants reported their pain level. For those who received the painkiller, the mean pain level was 4.8 and the standard deviation was 2.1. For those who received a placebo, the mean pain level was 5.5 and the standard deviation was 1.9. Can you conclude that the painkiller is effective? Perform an appropriate test at α = 0.01 with assuming that the homogeneity of variances assumption is satisfied.

• Which hypothesis test should be used?

 one-sample Z-test  one-sample t-test  independent-samples t-test  paired-samples t-test

• Step 1. State the hypotheses (both in words and in symbols)

• H₀: µ1 = µ2 (the paired sample means are equal)

• H₁: µ1 ≠ µ2 ("the paired sample means are not equal")

• Step 2: α = 0.01

• Find the critical value:

• Step 3: Calculate a test statistic and effect size (Cohen’s d). Show your work.
• Step 4: Make a decision.
• Step 5: State a conclusion (You should include the test statistic, p-value, effect size, and a verbal interpretation of the result).

Answer 1

We used an independent sample t-test

Detailed working is shown below

Conclusion : The pain killer has been effective in working as drug to reduce pain.