Question

Problem #3: A sample of 128 hypertensive people were given an anti hypertensive drug and the drug was found to be effective in 52 of those people. (By effective, we mean that their diastolic blood pressure is lowered by at least 10 mm Hg as judged from a repeat measurement taken 1 month after taking the drug.) (a) Find a 94% confidence interval for the true proportion of the sampled population for which the drug is effective (b) Using the results from the above mentioned survey, how many people should be sampled to estimate the true proportion of hypertensive people for which the drug is effective to within 3% with 98% confidence? (c) If no previous estimate of the sample proportion is available, how large of a sample should be used in (b)? confidence interval enter your answer in the form a,b (numbers correct to 3 decimals) Problem #3(a): Problem #3(b): How many should be sampled? Problem #3(c): How many should be sampled?

Answer 1

Ans:

a)z value for 94% confidence interval is 1.88

sample proportion=52/128=0.406

94% confidence interval for proportion is

=0.406+/-1.88*SQRT(0.406*(1-0.406)/128)

=0.406+/-0.082

=(0.325, 0.488)

b)

Margin of error=0.03

sample size,n=2.326^2*0.406*(1-0.406)/0.03^2=1450

c)

sample size,n=2.326^2*0.5*(1-0.5)/0.03^2=1503