Question

A sample of 127 hypertensive people were given an anti-hypertensive drug. The drug was effective in 73 of the sample (Effective meaning blood pressure was reduced by 10 or more after a repeat assessment (1 month after taking drug).

1) Find the 92% confidence interval for the true proportion of the sampled population for which the drug is effective. (3 decimals)

2) Using the results from the above survey, how many people should be sampled to estimate the true proportion of hypertensive people for which the drug is effective to within 2% with 95% confidence?

Answer 1

a)

p̂ = X / n = 73/127 = 0.575
p̂ ± Z(α/2) √( (p * q) / n)
0.575 ± Z(0.08/2) √( (0.5748 * 0.4252) / 127)
Z(α/2) = Z(0.08/2) = 1.751
Lower Limit = 0.575 - Z(0.08) √( (0.5748 * 0.4252) / 127) = 0.498
upper Limit = 0.575 + Z(0.08) √( (0.5748 * 0.4252) / 127) = 0.652
92% Confidence interval is ( 0.498 , 0.652 )

b)

p̂ = X / n = 73/127 = 0.5748

Sample size = Z2(α/2) * p̂ ( 1 - p̂) / E2

= 1.75072 * 0.5748 ( 1 - 0.5748) / 0.022

= 1872.7

n = 1873 (Rounded up to nearest integer)