Question

Suppose a clinical trial is conducted to test the efficacy of a drug ! for treating gonorrhea in females. 100 female patients with gonorrhea are given this drug and are seen 2 weeks later, at which time 10 of the 100 patients still have gonorrhea.

A.) What is the best point estimate for p, the probability of a failure with the drug A?

5%

10%

15%

20%

B) What is the Standard error of the point estimate?

10%

9%

5%

3%

C) Based on the Normal Approximation, what is the 95% Confidence Interval for p?

(0.488, 0.688)

(0.041, 0.688)

(0.128, 0.348)

(0.041, 0.159)

D.) For a drug to be considered effective, the gonorrhea rate after treatment needs to be lower than 15%. Based on this and the previous information in part c, would drug A be considered effective? (Yes or No?)

Answer 1

A)

best point estimate for p is the :

Sample proportion : = Number of patients still have gonorrhea / Total number of patients with gonorrhea who are given this drug = 10/100 = 0.10

best point estimate for p, the probability of a failure with the drug A = 0.10 x 100 = 10%

Ans : 10%

B)

Standard error of the point estimate : SE

n : Sample Size : Total number of patients with gonorrhea who are given this drug = 100

Standard error of the point estimate = 0.03* 100 = 3%

Ans : 3%

C)

95% Confidence Interval for p :

for 95% confidence level = 100 - 95/100 = 0.05

/2 = 0.05/2 = 0.025

Z_0.025 = 1.96

95% Confidence Interval for p :

95% Confidence Interval for p : (0.041,0.159)

Ans : (0.041, 0.159)

D)

95% Confidence Interval for p in terms of percentage = (0.041*100, 0.159*100) =(4.1%,15.9%)

Lower Confidence limit = 4.1%

Upper confidence limit = 15.9%

For a drug to be considered effective, the gonorrhea rate after treatment needs to be lower than 15%;

Since upper confidence limit 15.9 is greater than 15% ; drug A is not considered effective.

would drug A be considered effective? No

Ans : No