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
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
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