Question

the manager of a grocery store wants to determine what proportion of people who enter his store are his regular customers. what size sample should he take so that at 99% the margin of error will not be more than 0.1?

Answer 1

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

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)*(2.58/0.1)^2
n = 166.41

Therefore, the sample size needed to satisfy the condition n >= 166.41 and it must be an integer number, we conclude that the minimum required sample size is n = 167
Ans : Sample size, n = 167