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 17 minutes. How large a sample should she take to estimate the mean time to within 2 minutes with 94% confidence?

Sample Size =

Answer 1

Solution :

Given that,

standard deviation = = 17

margin of error = E = 2

At 94% confidence level the z is ,

= 1 - 94% = 1 - 0.94 = 0.06

/ 2 = 0.06 / 2 = 0.03

Z_/2 = Z_0.05 = 1.88

Sample size = n = ((Z_/2 * ) / E)²

= ((1.88 * 17) / 2)²

= 255.36 = 256

Sample size = 256