1. A researcher developed a painkiller and wanted to test itseffect. He recruited a group of 20 people who suffer from chronicpain of a similar level. Among these 20 participants, 10participants received the painkiller and the other 10 participantsreceived a placebo. One hour after taking the pills, theparticipants reported their pain level. For those who received thepainkiller, the mean pain level was 4.8 and the standard deviationwas 2.1. For those who received a placebo, the mean pain level was5.5 and the standard deviation was 1.9. Can you conclude that thepainkiller is effective? Perform an appropriate test at ? = 0.01with assuming that the homogeneity of variances assumption issatisfied.

• Which hypothesis test should be used?

? one-sample Z-test ? one-sample t-test ?independent-samples t-test ? paired-samplest-test

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

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

• H₁: µ1 ? µ2 ("the paired sample means are notequal")

• Step 2: ? = 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 teststatistic, p-value, effect size, and a verbal interpretation of theresult).