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 80% 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.

Answer 1

Solution :

Given that,

= 1 - = 0.5

margin of error = E = 0.06

At 80% confidence level

= 1 - 80%

=1 - 0.80 =0.20

/2 = 0.10

Z/2 = 1.282

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

= (1.282 / 0.06)² * 0.5 * 0.5

= 114.13

sample size = n = 115