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 6 percentage points of the true population proportion of customers who are males?

z0.10	z0.05	z0.04	z0.025	z0.01	z0.005
1.282	1.645	1.751	1.960	2.326	2.576

Use the table of values above.

Provide your answer below:

Answer 1

Solution:

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 6% = 0.06

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

Sample size = n = ((Z _{/ 2}) / E)² * * (1 - )

= (1.960 / 0.06)² * 0.5 * 0.5

= 266.77

= 267

n = sample size = 267