Question

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.23. How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 99% confidence level with an error of at most 0.03? Round your answer up to the next integer.

Answer 1

Solution :

Given that,

= 0.23

1 - = 0.77  

margin of error = E = 0.03

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= (2.576 / 0.03)² * 0.23 * 0.77

= 1305.77

sample size = 1306