Question

# A quality-control engineer wants to find out whether or not a new machine that fills bottles...

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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