Statistics 3301

Question

Suppose the manager of a shoe store wants to determine the current percentage of customers who are males. How many customers should the manager survey in order to be 95% confident that the estimated (sample) proportion is within 8 percentage points of the true population proportion of customers who are males?

Z 0.10 Z 0.05 Z 0.04 Z 0.025 Z 0.01 Z 0.005

1.282 1.645 1.751 1.960 2.326 2.576

Answer ________

Answer 1

this is a 2-sided ci, so use .025 = (100%-95%)/2

z = 1.96

For the binomial dist., the sample mean has variance p(1-p)/n, which has maximum variance when p = .5

Thus, .08 = 1.96 σ = 1.96 * .5 / √n

.08 √n = .98

√n = 12.25

n = 12.25² = 150.0625

One normally takes the ceiling here rather than round, so n = 151