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 their contents. She obtains the following results:

Old Machine	New Machine
16.01	16.02
16.04	15.96
15.96	16.05
16	15.95
16.07	15.99
15.89	16.02
16.04	16
16.05	15.97
15.91	16.03
16.1	16.06
16.01	16.05
16	15.94
15.92	16.08
16.16	15.96
15.92	15.95

a) is the variability in the new machine less than that of the old machine at the alpha=0.05 level of significance? Note: normal probability plots indicate that the data are normally distributed

b) draw boxplots of each data set to confirm the results of part a visually

Answer 1

a)

using Excel

data -> data analysis

F-Test Two-Sample for Variances
	Old Machine	New Machine
Mean	16.00533333	16.002
Variance	0.005755238	0.002102857
Observations	15	15
df	14	14
F	2.736865942
P(F<=f) one-tail	0.034842463
F Critical one-tail	2.483725741

p-value for one-tailed test = 0.034 < alpha

hence we reject the null hypothesis

we conclude that there the variability in the new machine less than that of the old machine