Question

You are testing a new package handling system. The Historical average is 35 minutes with a population standard deviation of 8 minutes. A test of the new process on 10 random runs has a mean of 33 minutes.

Let’s say 33 was in fact the true mean of the alternative hypothesis – in other words an infinite number of sample means at the new process would have resulted in a mean of 33? What is the beta error and power of this experiment? (note: this one is difficult. Draw a picture of the alternative hypothesis)

A)Beta 50%, Power 50%

B)Beta 20%, Power 80%

C)Beta 80%, Power 20%

D)Beta 40%, Power 40%

Answer 1

We will assume that the significance level is 0.05

. This is a left tailed test.

We will fail to reject the null (commit a Type II error) if we get a Z statistic greater than -1.64

This -1.64 Z-critical value corresponds to some X critical value ( X critical), such that

So I will incorrectly fail to reject the null as long as a draw a sample mean that greater than 30.84. To complete the problem what I now need to do is compute the probability of drawing a sample mean greater than 30.84 given

µ = 33. Thus, the probability of a Type II error is given by

hence or 80% and the power is or 20%