A hypothesis testing situation is given. The population standard deviation, sample size, and significance level are given. Complete the table to give the probability of a Type II error and the power for each of the given values of μ. Use the table to draw the power curve.
A hypothesis test is to be performed to determine whether the mean waiting time during peak hours for customers in a grocery store has increased from the previous mean waiting time of
Preliminary data analyses indicate that it is reasonable to apply a
The hypotheses are
H
0: μ = 8.3 minutes
H
a: μ > 8.3 minutes.
The population standard deviation is 3.6 minutes. The sample size is 45. The significance level is 0.05. Find the probability of a Type II error and the power for μ = 8.4, 8.6, 8.8, 9.0, 9.2, 9.4, 9.6, 9.8, 10.0, 10.2.
| True mean P(Type II error) | Power |
μ β 1 - β
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0
10.2
Power Curve
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