A sample of 140 hypertensive people were given an
anti-hypertensive drug, and the drug was found to
be effective in 57 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 93% 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 1%
with 99% confidence?
(c)
If no previous estimate of the sample proportion is available,
how large of a sample should be used
in (b)?