Exercise 1
The inside diameter of metal washers has a variance of 0.000125 cm2
or less when
the process by which they are made is under control. A random
sample of 31 washers
taken from the assembly line yields a variance of 0.000155
cm2.
Based on this information, perform the following tasks. Do all
calculations ‘manually’
(i.e., with a hand calculator without using R, Excel or any other
software), showing the
relevant formulas and the major steps.
(a) (8 marks)
Estimate and interpret the population variance of the inside
diameters of all metal
washers manufactured during this shift with 90% confidence.
(b) (10 marks)
Do these data provide sufficient information to indicate at the 5%
significance level
that the process is out of control? Briefly discuss the steps of
the test you perform
showing all relevant details.
(c) (8 marks)
What assumption(s) must you make to validate the confidence
interval and the
hypothesis test in parts (a) and (b)? Are they likely satisfied?
Explain your answer.