Question

A charitable organization wishes to estimate, to within half a percentage point, the proportion of all telephone solicitations to its donors that result in a gift, with 90% confidence. Estimate the minimum sample size required, using the information that in the past the response rate has been about 30%.

Answer 1

Solution:

Given,

E = 0.5% = 0.005

c = 90% = 0.90

p = 30% = 0.30

1- p = 1 - 0.30 = 0.90

Now,

= 1 - c = 1 - 0.90 = 0.10

/2 = 0.05

= 1.645 (using z table)

The sample size for estimating the proportion is given by

n =

= (1.645)² * 0.30 * 0.70 / (0.005²)

= 22730.61

= 22731 ..(round to the next whole number)

Minimum sample size = 22731