Question

A Popeyes store manager wants a 90% confidence interval to estimate the proportion of customers who...

A Popeyes store manager wants a 90% confidence interval to estimate the proportion of customers who have tried their new chicken sandwich. She is also seeking a half-length of no more than 0.05 (B = 0.05). How many customers does the manager need to survey? (NOTE: Express the MULTIPLIER to three decimal places for your calculation & assume the MOST conservative estimate for the proportion.)

The following information is provided,
Significance Level, α = 0.1, Margin of Error, E = 0.05

Assume estimate of proportion p is, p = 0.5
The critical value for significance level, α = 0.1 is 1.645.

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)*(1.645/0.05)^2
n = 270.6

Therefore, the sample size needed to satisfy the condition n >= 270.6 and it must be an integer number, we conclude that the minimum required sample size is n = 271
Ans : Sample size, n = 271