The graph below displays power for a one-sample Z-test of the null hypothesis
that the population mean is 50. The red distribution is the sampling distribution
of the mean assuming the null hypothesis is true. The blue distribution is the sampling distribution of the mean
assuming the population mean is 70. A sample mean over 58 is significantly greater than 50 at the 0.05 level. The shaded area in the red distribution is

The area shaded in red is the probability of getting a mean that is significantly different from 50 if the null hypothesis is true.
questions/power2.gif
true
Type I error rate
false
Power
The graph below displays power for a one-sample Z-test of the null hypothesis
that the population mean is 50. The red distribution is the sampling distribution
of the mean assuming the null hypothesis is true. The blue distribution is the sampling distribution of the mean
assuming the population mean is 70. A sample mean over 58 is significantly greater than 50 at the 0.05 level. The shaded area in the blue distribution is

The area shaded in red is the probability of getting a mean that is significantly different from 50 if the population mean is 70.
questions/power2.gif
false
Type I error rate
true
Power
The graph below displays power for a one-sample Z-test of the null hypothesis
that the population mean is 50. The red distribution is the sampling distribution
of the mean assuming the null hypothesis is true. The blue distribution is the sampling distribution of the mean
assuming the population mean is 70. A sample mean over 58 is significantly greater than 50 at the 0.05 level. If the blue distribution had a mean of 75 instead of 70 then:

The Type I error rate would not increase since that is a function of the red distribution. Power would increase since
more of the blue distribution would be to the right of the cutoff. The two distributions would overlap less, but would still overlap.
The cut-off point for significance is not a function of the blue distribution.
questions/power2.gif
false
The Type I error rate would increase
true
Power would increase
false
The two distributions would not overlap.
false
The cut-off point for significance would increase.
The graph below displays power for a one-sample Z-test of the null hypothesis
that the population mean is 50. The red distribution is the sampling distribution
of the mean assuming the null hypothesis is true. The blue distribution is the sampling distribution of the mean
assuming the population mean is 70. A sample mean over 58 is significantly greater than 50 at the 0.05 level. If the standard deviation were reduced then:

The Type I error rate is not a function of the standard deviation. Power would increase since
the overlap of the distributions would decrease and the cutoff point would decrease.
The cut-off point for significance would be reduced because a smaller distance from the red distributions mean is needed to be significant.
questions/power2.gif
false
The Type I error rate would increase
true
Power would increase
true
The cut-off point for significance would decrease.