Let X1X25 be a random sample from a normal distribution with

Let X1,...,X25 be a random sample from a normal distribution with variance 100. Find the rejection region for a test at level alpha = 0.10 of H0: mu = 0 against Ha: mu = 1.5. What is the power of the test?

Solution

Power and Sample Size

1-Sample t Test

Testing mean = null (versus not = null)
Calculating power for mean = null + difference
Alpha = 0.1 Assumed standard deviation = 10

Sample
Difference Size Power
1.5 25 0.188659