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.

A) 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.

B) 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.

C) 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.

D) 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

Given :-

Experimental --

n1 = 100

X1= 38

P1^ = (x1/n1)

Placebo --

n2 =100

x2 = 21

P2^ = (x2/n2)

P^ = (x1+x2)/(n1+n2)

Using ti-83 calculator.

Test statistic :

Z = 2.64

And critical value = 1.960

Rejection region for two tailed test is

R ={ z , |z| >= 1.960}

Test statistic value is not in rejection region. i.e. 2.74>= 1.96

then reject H0.

#Answer :-

A) We reject H0 at the 5% level because 2.64 is greater than 1.96. We do have statistically significant evidence at alpha= 0.05 to show that there is a difference in the proportions of patients reporting a reduction in symptoms.