Question

A researcher wishes to test a hypothesis, using a 5% level of significance, to see if the average level of cholesterol can be reduced from using a medical treatment for a particular population. If one wishes to perform a one-side one-sample t test, and wishes that the t test to have a power of 0.80 to detect a reduction of 10mg/100ml in cholesterol (LDL), how large a sample would be needed? (From a pilot study, the estimated standard deviation of the cholesterol levels to this population is 30)

Answer 1

For calculating the sample size(n) we need the following information

sig.level= 5% = 0.05 (type I error)

power of the test = 0.80 (1 - type II error)

delta = difference or reduction between two mean = 10 mg/100ml

sigma= sample standard deviation=30

These five parameters are related to each other if one is unknown then it can be calculated from the other three.

Now the sample size can be obtained by using the simple R command

power.t.test(n=NULL,delta = 10,sd=30,power = 0.8,sig.level = 0.05,type = "one.sample")

the output is

One-sample t test power calculation

n = 72.58407
delta = 10
sd = 30
sig.level = 0.05
power = 0.8
alternative = two.sided

so the sample size(n) is 73 (approximated)