Question

The Office of Public Works (OPW) wants to estimate the proportion of "STOP" signs in Sacramento
that need to be repaired or replaced. The OPW is confident that the proportion is not more than
20%. If the OPW wants to be 90% confident that the proportion in a random sample will be within
1 percentage point of the actual proportion that needs repair or replacement, how big should the
sample be to satisfy the OPW's objectives?

Answer 1

The following information is provided,
Significance Level, α = 0.1, Margin of Error, E = 0.01

The provided estimate of proportion p is, p = 0.2
The critical value for significance level, α = 0.1 is 1.64.

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 = 0.2*(1 - 0.2)*(1.64/0.01)^2
n = 4303.36

Therefore, the sample size needed to satisfy the condition n >= 4303.36 and it must be an integer number, we conclude that the minimum required sample size is n = 4304
Ans : Sample size, n = 4304 or 4303