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 200 participants who received the new medication, 75 reported pain relief, while 60 out of the 200 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.

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 200 participants who received the new medication, 75 reported pain relief, while 60 out of the 200 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.