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 0.18. 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 98% confidence level with an error of at most 0.02? Round your answer up to the next integer.

Answer 1

The following information is provided,
Significance Level, α = 0.02, Margin of Error, E = 0.02

The provided estimate of proportion p is, p = 0.18
The critical value for significance level, α = 0.02 is 2.33.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.18*(1 - 0.18)*(2.33/0.02)^2
n = 2003.26

Therefore, the sample size needed to satisfy the condition n >= 2003.26 and it must be an integer number, we conclude that the minimum required sample size is n = 2004
Ans : Sample size, n = 2004