STAT412

and Power Calculations
In-Class Exercise

Suppose you want to test H o
:

=1,000 against H a
:

>1,000 using

=.025. The population in question is normally distributed with standard deviation 120. A random sample of size n=36 will be used. a.
Sketch the sampling distribution of x assuming that H o
is true. b.
Find the value of x o , that value of x above which the null hypothesis will be rejected. Indicate the rejection region on your graph of part a . Shade the area above the rejection region and label it

. c.
On your graph of part a , sketch the sampling distribution of x if

=1,030. Shade the area under this distribution that corresponds to the probability that x falls in the nonrejection region when

=1,030, Label this area

. d.
Find

. e.
Find the power of the test. f.
If

=1,050 instead of 1,030, what is the probability that the test will incorrectly fail to reject H what is

? o
? That is, g.
If

=1,050 instead of 1,030, what is the probability that the test will correctly reject the null hypothesis?
That is, what is the power of the test? h. What do you learn?