Question

1. A clinical trial is conducted to compare an experimental medication to placebo to reduce the symptoms of asthma. Two hundred participants are enrolled in the study and randomized to receive either the experimental medication or placebo. The primary outcome is self-reported reduction of symptoms. Among 100 participants who receive the experimental medication, 38 report a reduction of symptoms as compared to 21 participants of 100 assigned to placebo. Is there a significant difference in the proportions of participants reporting a reduction of symptoms between the experimental and placebo groups? Use α=0.05. Step 1. Set up hypotheses and determine level of significance Step 2. Select the appropriate test statistic Step 3. Set up decision rule Step 4. Compute the test statistic Step 5. Conclusion

Answer 1

Step 1:

Level of significance (alpha) = 0.05

test hypothesis Ho: p1 = p2 Vs. Ha : p1 p2

Step 2:

This corresponds to a two-tailed test, for which a z-test for two population proportions needs to be conducted.

Step3:

Based on the information provided, the significance level is \alpha = 0.05α=0.05, and the critical value for a two-tailed test is z_c = 1.96zc​=1.96.

The rejection region for this two-tailed test is

R = { z: ∣z∣>1.96 }

Step 4:

Step 5:

Since it is observed that ∣z∣=2.636 > zc​=1.96, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0084, and since p=0.0084 < 0.05, it is concluded that the null hypothesis is rejected.

Therefore, there is significant difference in the proportions of participants reporting a reduction of symptoms between the experimental and placebo groups.