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%
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%
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