Question

A survey states that 280 out of 800 people smoke on a regular basis. Determine the required sample size if you want to be 90% confident that the sample proportion is within 3% of the population proportion.

Answer 1

The following information is provided,
Significance Level, α = 0.1, Margin of Error, E = 0.03

The provided estimate of proportion p is, p = 0.35
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 = 0.35*(1 - 0.35)*(1.64/0.03)^2
n = 679.87

Therefore, the sample size needed to satisfy the condition n >= 679.87 and it must be an integer number, we conclude that the minimum required sample size is n = 680
Ans : Sample size, n = 680 or 679