Question

A random sample of elementary school children in New York state is to be selected to estimate the proportion pp who have received a medical examination during the past year. It is desired that the sample proportion be within 0.035 of the true proportion with a 9999% 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 pp is available, approximately how large of a sample size is needed?
Don't forget to round up.
n=n=

(b)    If a planning study indicates that pp is around 0.80.8, approximately how large of a sample size is needed?
Don't forget to round up.
n=n=

Answer 1

Solution :

Given that,

= 0.5 ( use 0.5)

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.035

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.5758    ( Using z table )

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

= (2.5758 / 0.035)2 * 0.5 * 0.5

=1354.029

Sample size = 1354

(B)

Solution :

Given that,

= 0.8

1 - = 1 - 0.8 = 0.2

margin of error = E = 0.035

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.5758    ( Using z table )

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

= (2.5758 / 0.035)2 * 0.8 * 0.2

=866.57

Sample size = 867