Question

A random sample of elementary school children in New York state is to be selected to estimate the proportion p who have received a medical examination during the past year. It is desired that the sample proportion be within 0.02 of the true proportion with a 98% level of confidence, (Be sure to use four or five decimals of accuracy for all values used in the calculations, including the z-score) (a) Assuming no prior information about p is available, approximately how large of a sample size is needed? Don't forget to round up. n= (b) If a planning study indicates that p is around 0.2, approximately how large of a sample size is needed? Don't forget to round up. n=

Answer 1

Solution:

Given that,

= 0.2

1 - = 1 - 0.2 = 0.8

margin of error = E = 0.02

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z_0.025 = 2.3260

Sample size = n = ((Z _{/ 2}) / E)² * * (1 - )

= (2.3260/ 0.02)² * 0.2 * 0.8

= 2164.1104

= 2164

n = sample size = 2164