What parameters increase or decrease POWER?
This demo illustrates how the Power of a hypothesis test increases or decreases as certain
parameters change.
The following is the null and alternated hypothesis used in this demo.
Ho : μ = 8
Ha: μ > 8
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Fathom graphed a red sampling distribution that is normally distributed with the
2
hypothesized mean of 8 and a standard deviation of
.
n
The blue distribution represents the true distribution of sample means of size n from the
actual distribution with mean, mu.
The black line represents the critical point, the point at which the null hypothesis will be
rejected.
*** The power of the hypothesis test is the area shaded to the right of the black line under the
blue distribution. This area represents all the samples that would reject the null hypothesis if the
true population mean does not equal 8.
Step I.
Observe that the population mean, mu, equals 10.0. Change the other parameters by moving the
sliders and notice how the distributions change.
a.) Which parameters increase or decrease the power of the hypothesis test?
b.) Describe how each parameter would increase the Power of a hypothesis test.
Step II. Now change the mu to be anything other than 8. Move the slider for mu and notice if
the power increases or deceases.
c.) Describe how the Power of the test changes as the mu move further away from the
hypothesis mean of 8.
*** If the red and the blue distribution are the same, then the true population mean is 8. This
would mean that the null hypothesis is true. When the two distributions are the same then the
area to the right of the line represents type I error. This area represents samples that would
cause you to reject the null hypothesis even though the null hypothesis is true.
Step III. Move the slider for mu to 8. Move the other sliders to see what parameters decrease
type I error.
d.) How do the other parameters decrease type I error?
Following-up Questions:
1. According to the sod store problem from the previous demo what type of error is worse,
type I or type II?
2. If you were the owner and wanted to decrease the chances of type II error but did not
want to sacrifice correct decisions from being made, what would you suggest for the
sample size and alpha for a hypothesis test?