Question

A sample of 102 hypertensive people were given an anti-hypertensive drug, and the drug was found to be effective in 70 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 90% 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 97% confidence?

Answer 1

Solution :

Given that,

a) Point estimate = sample proportion = = x / n = 70 / 102 = 0.686

1 - = 1 - 0.686 = 0.314

Z/2 = Z0.05 = 1.645

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.645 (((0.686 * 0.314) / 102 )

= 0.076

A 90% confidence interval for population proportion p is ,

± E   

= 0.686  ± 0.076

= ( 0.610, 0.762 )

b) Z/2 = Z0.015 = 2.17

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.17 / 0.01)2 * 0.686 * 0.314

= 10143.15

sample size = n = 10144