Question

A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 6%

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.06

The provided estimate of proportion p is, p = 0.5
The critical value for significance level, α = 0.05 is 1.96.

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 = 0.5*(1 - 0.5)*(1.96/0.06)^2
n = 266.78

Therefore, the sample size needed to satisfy the condition n >= 266.78 and it must be an integer number, we conclude that the minimum required sample size is n = 267
Ans : Sample size, n = 267