Exercise 1 indicates that power is relatively low with only n = 10 observations. Imagine that you want power to be at least .8. One way of getting more power is to increase the sample size, n. Verify that for sample sizes of 20, 30, and 40, power is .56, .71, and .81, respectively.
Exercise 1
For Exercise 2, verify that power is .35 if µ = 46.
Exercise 2
A manufacturer of medication for migraine headaches knows that their product can cause liver damage if taken too often. Imagine that by a standard measuring process, the average liver damage is µ = 48. A modification of their product is being contemplated, and, based on n = 10 trials, it is found that X‾ = 46. Assuming σ = 5, they test H0 :µ ≥ 48, the idea being that if they reject, there is convincing evidence that the average amount of liver damage is less than 48. Then
Z = (46 - 48)/ (5/√(10)) = -1.3.
With α = .05, the critical value is -1.645, so they do not reject, because Z is not less than the critical value. What might be wrong with accepting H0 and concluding that the modification results in an average amount of liver damage greater than or equal to 48?