Answer.....

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? 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 16.0 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 Let o1 denote the standard deviation for the new machine, and 72 denote the standard deviation for the old machine. Conditions: In Minitab Express, perform a normality test on each sample. In the normal probability plot for the new machine, the data (do / do not) follow the reference line throughout. The P-values for the Anderson-Darling for the new machine is (Do not round.) In the normal probability plot for the old machine, the data (do / do not) follow the reference line throughout. The P-values for the Anderson-Darling for the new machine is (Do not round.) The necessary conditions for the F-test (are / are not) satisfied. Test Statistic: The test statistic for this test is Fo = (Do not round.) Rejection Region: I've will perform a (left / right / two) -tailed test The appropriate critical value(s) for this test is/are (Round to 3 decimal places. If there are two critical values, report both separated by only a single space.) On a separate sheet of paper, sketch the rejection region(s) for this test, and mark the locations of the critical value(s) and test statistic. Conclusion: We (reject / fail to reject) Ho. The given data (does / does not) provide significant evidence that there is less variability in fill volumes from the new machine than from the old machine. P-Value: The P-value for this test is (Do not round.)