Question

A medical researcher wants to investigate the amount of time it takes for patients' headache pain to be relieved after taking a new prescription painkiller. She plans to use statistical methods to estimate the mean of the population of relief times. She believes that the population is normally distributed with a standard deviation of 19 minutes. How large a sample should she take to estimate the mean time to within 5 minutes with 92% confidence?

Sample size=

Answer 1

Solution

standard deviation =   =19

Margin of error = E = 5

At 92% confidence level the z is ,

= 1 - 92% = 1 - 0.92 = 0.08

/ 2 = 0.04

Z/2 = Z0.04 =1.75

sample size = n = [Z/2* / E] 2

n = ( 1.75* 19/ 2)2

n =276.39

Sample size = n =277