Question

The pediatrician's office would like to estimate the proportion of parents that will not allow their child to receive a new flu shot with 95% confidence. It is initially believed that 20% of parents will not allow their child to receive the flu shot. Using this information, what is the smallest number of parents that must be sampled in order for the estimate to be within 6% of the true proportion?

Answer 1

solution:

Given that,

= 20%=0.20

1 - = 1 - 0.20 = 0.80

margin of error = E = 6% = 0.06

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= (1.96 / 0.06)² * 0.20 * 0.80

= 170.73

Sample size = 171