Question

Reading proficiency: An educator wants to construct a 99% confidence interval for the proportion
of elementary school children in Colorado who are proficient in reading.

(b) Estimate the sample size needed if no estimate of P is available.

A sample of __ elementary school children is needed to obtain a 99% confidence interval
with a margin of error of 0.03.

Answer 1

Solution :

Given that,

= 0.5 ( assume 0.5)

1 - = 1 - 0.5 = 0.5

margin of error = E =0.03

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576 ( Using z table )

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

= (2.576 / 0.03)2 * 0.5 * 0.5

=1843.27

Sample size = 1844