To find power of the test statistic, Type II error and sample size
The Product Design & Marketing Departments have agreed to consider changing the material used for the handle of an ax produced by their firm for consumer use. The material currently used is hickory (wood). They are contemplating, primarily for reasons related to cost, the use of a composite material; produced by an overseas supplier.
One of the critical product performance characteristics for the handle is resistance to splitting &/or breakage during use, measured in the laboratory with an impact test. This is, as you might expect, a destructive test; and is expensive to run. Historically, the hickory handles have yielded the following parameters for this characteristic:
μ = 110 lbs.
σ = 2 lbs.
γ3 = 0.0
γ4 = 0.0
A sample of 9 of the new composite handles were tested in the impact test, and yielded the standard deviation (snew) of 2.1 lbs.; subsequent statistical analysis allowed the researcher to infer that there had been no change in the variability of the impact resistance of the new handles from the results exhibited by the old (wooden) handles.
problems:
assume that a difference (Δ) of 2 lbs. in the mean was important to detect, a maximum Type I Error (α) level of 5 percent, and the desire to run a two-tailed test, then
A. What is the Power of test?
B. What is β?
C. In your mind, are these values acceptable? Why? Why not?
D. If a maximum β of 1 percent was required, what must the sample size have been?