Question

 

A clinical trial is conducted comparing a new pain reliever for arthritis to a placebo. Participants are randomly assigned to receive the new treatment or a placebo and the outcome is pain relief within 30 minutes. Of the 120 participants who received the new medication, 44 reported pain relief, while 21 out of the 120 participants who received the placebo reported pain relief. Is there a significant difference in the proportions of patients reporting pain relief? Run the test at a 5% level of significance.

Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You MUST show your work to receive full credit.

Answer 1

The proportion of patients who received the medication and reported pain relief (p1) = 44/120

The proportion of patients who received the placebo and reported pain relief (p2) = 21/120

Step-1: The null hypothesis is that both the proportions are equal, i.e. p1=p2 and the alternate hypothesis is that the two proportions are not equal, i.e.

Step-2: The appropriate test for this particular problem would be to perform a 'large-sample proportion test' for the null hypothesis since the sample size of 120 can be considered as large.

Step-3: We compute the test statistic as,

Since we are looking at a 5% level of significance, the alpha is 0.05. The decision rule is that we accept the alternate hypothesis if:

i.e.

Step-4: On using the above formula for computing test-statistic, we get

Step-5: The critical value is -1.96 and since z=-2.3203<-1.96, we reject the null hypothesis and conclude that the medicine actually had an impact on the population.