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 a-0.05 level of significance? 16.01 16.04 15.96 16.00 16.07 ld Machine 15.89 16.04 16.05 15.91 16.10 16.01 16.00 15.92 16.16 15.92 16.00 15.95 16.00 16.06 16.08 ew Machin 15.96 15.99 15.97 16.05 15.96 16.05 16.02 16.02 15.94 15.95 To make this a right-tailed test, let σ1 denote the standard deviation of fill volumes from the deviation of fill volumes from the other machine (old / new) machine, and σ2 the standard Conditions In Minitab Express, enter the given data in two separate columns, and perform an normality are conditions for the F-test test on each sample. The P-values for the Anderson-Darling tests of for the sample from the new machine. The necessary for the sample from the old machine, and (are / are not) satisfied Rejection Region: Recall that we are performing a right-tailed test. The appropriate critical value for this test is Fa- in the table. Remember to practice sketching the rejection region.) (Report critical values as they appear

Answer 1

old

p-value for old =

0.6513

p-value for new =

0.3422

conditions are satisfied

critical value = 2.4837

TS = 2.8172

we reject the null

the data does provide evidence

p-value = 0.0312