Question

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. When you test if there is a significant difference in the proportions of participants reporting a reduction of symptoms between the experimental and placebo groups. Use α = 0.05. What should the researcher’s conclusion be for a 5% significance level? Reject H₀
because 2.64 ≥ 1.960. We have statistically significant evidence at α = 0.05 to show that there is a difference in the proportions of patients reporting a reduction in symptoms.

		We reject H0 at the 5% level because 2.64 is greater than 1.96. We do have statistically significant evidence at α = 0.05 to show that there is a difference in the proportions of patients reporting a reduction in symptoms.
		We fail to reject H0 at the 5% because -2.64 is less than 1.645. We do not have statistically significant evidence to show that there is a difference in the proportions of patients reporting a reduction in symptoms.
		We fail to reject H0 at the 5% because -2.64 is less than 1.96. We do have statistically significant evidence at α = 0.05 to show that there is a difference in the proportions of patients reporting a reduction in symptoms.
		We fail to reject H0 at the 5% because 2.64 is greater than -1.645. We do have statistically significant evidence at α = 0.05 to show that there is a difference in the proportions of patients reporting a reduction in symptoms.

Answer 1

Let p1 be the proportion of participants who receive the experimental medication and reported a reduction of symptoms.

Given = 38/100 = 0.38

= 21/100 = 0.21

We need to check if there is significant difference in the proportions.

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

So accordingly the null and the alternate hypothesis would be:

pooled proportion = (38+21)/200 = 59/200 = 0.295

Standard error (SE) = = 0.064

Z-statistic would be = (0.38-0.21)/0.064 = 2.64

And for a significance level of 0.05, critical value of z = 1.96.

=> Reject Ho if z-statistic > 1.96

And z-statistiic = 2.64 > 1.96 , Hence reject Ho.

=> We have strong evidence against the null hypothesis and claim that the proportions are not equal.

=> Option 1 is correct.