A study examined the effectiveness of Botox injections in the corrugator supercilii muscles for the treatment of chronic migraines. Of the 29 migraine-prone patients participating in the study, 16 reported complete migraine elimination. How large a sample n would you need to estimate p with margin of error 0.02 with 90% confidence? Use the guess p* = 0.50 as the value for p.

Question

Quizplus · Accepted Answer

We know that the margin of error (E) is 0.02 and the confidence level (CL) is 90%. We also have to use the guess p* = 0.50. 
We can use the formula: 
n = [(z^2 * p* * (1-p*)) / E^2]
where z is the z-score for the given confidence level. For a 90% confidence level, the z-score is 1.645. 
Plugging in the values: 
n = [(1.645^2 * 0.50 * 0.50) / 0.02^2]
n = 1691.87
Rounding up gives us the answer of n = 1692.

A Study Examined the Effectiveness of Botox Injections in the Corrugator