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 24 minutes. How large a sample should she take to estimate the mean time to within 5 minutes with 90% confidence?

Answer 1

Solution :

Given that,

Population standard deviation = = 24

Margin of error = E = 5

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

sample size = n = (Z_/2* / E) ²

n = (1.645 * 24 / 5 )²

n = 62.35

n = 63

Sample size = 63