Question

Find the minimum sample size for the following. You wish to estimate with 90% confidence and within 3% of the true population, the proportion of senior citizens that need to be treated for heart disease. There is no initial estimate for p-hat.

Answer 1

Solution :

Given that,

= 0.5 ( when estimate is not given then use 0.5)

1 - = 1 - 0.5 = 0.5

margin of error = E = 3% = 0.03

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Sample size = n = (Z_/2 / E)² * * (1 - )

= (1.645 /0.03)² * 0.5 * 0.5

= 752

Sample size =752