Question

A local restaurant wants to determine what proportion of their customers prefer red wine with dinner instead of white wine. If they use a 99% level of confidence, how many customers do they need to survey to be within 2.5% of the true proportion?

Answer 1

The following information is provided,
Significance Level, α = 0.01, Margin of Error, E = 0.025

The provided estimate of proportion p is, p = 0.5
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 = 0.5*(1 - 0.5)*(2.58/0.025)^2
n = 2662.56

Therefore, the sample size needed to satisfy the condition n >= 2662.56 and it must be an integer number, we conclude that the minimum required sample size is n = 2663

Ans : Sample size, n = 2663