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

The statistical software output for this problem is:

Two sample proportion summary hypothesis test: P proportion of successes for population 1 P2 proportion of successes for population 2 P.-P.: Difference in proportions HP-P = 0 H PI-P20 Hypothesis test results: Difference Countl Totall Count2 Total2 Sample Diff. Std. Err. Z-Stat P- 38 100 21 100 0.17 0.064494186 2.6358965 P-value 0.0084

Critical value at 5% significance level = -1.96, 1.96

Hence,

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.

Option A is correct.