Question

A quality-control engineer wants to find out whether or not a new machine that fills bottles with liquid has less variability than the machine currently in use. The engineer calibrates each machine to fill bottles with 16 ounces of a liquid. After running each machine for 5 hours, she randomly selects 15 filled bottles from each machine and measures the volume of their contents (in ounces). The resulting data is provided in the table below. Is the variability in the new machine less than that of the old machine at the α = 0.05 level of significance?

Old Machine			New Machine
16.01	15.89	16.01	16.00	15.96	16.05
16.04	16.04	16.00	15.95	15.99	16.02
15.96	16.05	15.92	16.00	15.97	16.02
16.00	15.91	16.16	16.06	16.05	15.94
16.07	16.10	15.92	16.08	15.96	15.95

Hypotheses:
a) To make this a right-tailed test, let σ₁ denote the standard deviation of fill volumes from the _____ (old / new) machine, and σ₂ the standard deviation of fill volumes from the other machine.

Conditions:
In Minitab Express, enter the given data in two separate columns, and perform a normality test on each sample.

b) The P-values for the Anderson-Darling tests of normality are ______ for the sample from the old machine, and ________for the sample from the new machine.

c) The necessary conditions for the F-test ______ (are / are not) satisfied.

d) Recall that we are performing a right-tailed test. The appropriate critical value for this test is F_α = _______. (Report critical values as they appear in the table. Remember to practice sketching the rejection region.)

Answer 1

a) To make this a right-tailed test, let σ1 denote the standard deviation of fill volumes from the  old  machine, and σ2 the standard deviation of fill volumes from the other machine.

b) The P-values for the Anderson-Darling tests of normality are 0.651 for the sample from the old machine, and 0.342 for the sample from the new machine.

c) The necessary conditions for the F-test are satisfied.(Since p-values are high for both data, we can consider the two dataset from normal populations)

d) we are performing a right-tailed test. The appropriate critical value for this test is Fα = 2.483726.