Question

In: Statistics and Probability

Suppose the manager of a shoe store wants to determine the current percentage of customers who...

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 99% confident that the estimated (sample) proportion is within 10 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

Solutions

Expert Solution

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 10% = 0.010

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576 ( Using z table )

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

= (2.576 / 0.010)2 * 0.5 * 0.5

=16589.44

Sample size = 16590 rounded

n=16590 customers

orchestra answered 2 years ago
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