Question

A clinical trial is run to evaluate the effectiveness of a new drug to prevent preterm delivery. A total of n=250 pregnant women agree to participate and are randomly assigned to receive either the new drug or a placebo and followed through the course of pregnancy. Among 125 women receiving the new drug, 24 deliver preterm and among 125 women receiving the placebo, 38 deliver preterm. Is there a significant difference in the proportions of women who deliver preterm who are taking the new drug verse the placebo? Run the appropriate test at a 5% level of significance.

A. State the null and alternative hypothesis, H₀ and H_a.

_B. Compute the appropriate test statistic.

C. Find the p-value.

D. Construct a 95% Confidence Interval for the difference between the proportion of preterm delivery between the new medication and the placebo.

E. State your conclusion in the context of the problem (does the new medication reduce preterm delivery?)

handwritten notes are preferred so I can follow along.

Answer 1

A)
H0: p1 = p2
Ha: p1 not equals p2

B)
p1cap = 24/125 = 0.1920
p2cap = 38/125 = 0.3040

pcap = (24 + 38)/250 = 0.2480

SE = sqrt(0.248*(1-0.248)*(1/125 + 1/125)) = 0.0546

Test statistic,
z = (0.192 - 0.304)/0.0546
z = -2.0513

C)
p-value = 0.0402

D)
CI = ((0.192 - 0.304) - 1.96*0.0546, (0.192 - 0.304) + 1.96*0.0546)
= (-0.2190, -0.0050)

E)
Reject H0
There are significant evidence to conclude that there is difference in the propotion