A metal lathe is checked periodically by quality control inspectors to determine
ID: 2956978 • Letter: A
Question
A metal lathe is checked periodically by quality control inspectors to determine whether it is producing machine bearings with a mean diameter of 0.5 inch. If the mean diameter of the bearings is larger or smaller than 0.5 inch, then the inspector concludes that the process is out of control and needs to be adjusted. Define the null and alternative hypotheses that could be used to test whether the bearing production process is out of control. And define Type I and Type II error regarding the inspector's conclusion.Choose corresponding definitions for each explanation.
Lable if a,b,c,d are either:
Type 1 error
Type 2 error
H0
Ha
a. True mean diameter of all bearings produced by the lathe is larger or smaller than 0.05 inches, so; the process is out of control
b. The process is in control, but the true mean diameter of all bearings produced by the lathe is larger or smaller than 0.05 inches
c. True mean diameter of all bearings produced by the lathe equals 0.05 inches, so; the process is in control
d. The process is out of control, but the true mean diameter of all bearings produced by the lathe equals 0.05 inches
Explanation / Answer
We define the following parameter:
m = True mean diameter (in inches) of all bearings produced by the lathe
If either m > .5 or m < .5, then the metal lathe's production process is out of control. Since we wish to be able to detect either possibility, the null and alternative hypotheses would be
H0: m = .5 (i.e., the process is in control)
Ha: m ¹ .5 (i.e., the process is out of control)
An alternative hypothesis may hypothesize a change from H0 in a particular direction, or it may merely hypothesize a change without specifying a direction.