Question

A philanthropic organisation sent free mailing labels and greeting cards to a random sample of 100,000  potential donors on their mailing list and received 5254 donations.

​(a) Give a 99​% confidence interval for the true proportion of those from their entire mailing list who may donate. ​(in percent form)

(b) A staff member thinks that the true rate is 5.6%. Given the confidence interval you​ found, do you find that rate​ plausible?

Answer 1

a) From standard normal tables, we have:
P(-2.576 < Z < 2.576) = 0.99

The sample proportion here is computed as:

p = x/n = 5254 / 100000 = 0.05254

Therefore the confidence interval here is obtained as:

This is the required 99% confidence interval for the true proportion of those from their entire mailing list who may donate

b) As the given 5.6% proportion is outside the above computed confidence interval, therefore the given rate should not be plausible given the 99% confidence interval.