Question

You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 99% confidence level and a margin of error of 3%. A pilot survey reveals that 8 of the 51 sampled hold two or more jobs. How many in the workforce should be interviewed to meet your requirements? (Round up your answer to the next whole number.) Number of persons to be interviewed

Answer 1

The following information is provided,
Significance Level, α = 0.01, Margin of Error, E = 0.03

The provided estimate of proportion p is, p = 0.1569
The critical value for significance level, α = 0.01 is 2.58.

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 = 0.1569*(1 - 0.1569)*(2.58/0.03)^2
n = 978.36

Therefore, the sample size needed to satisfy the condition n >= 978.36 and it must be an integer number, we conclude that the minimum required sample size is n = 979
Ans : Sample size, n = 979