6. A facility for bottling soft drinks uses two fill and seal machines. As part of quality control, data are periodically collected to test if the fill weight is the same for the two machines. A particular data collection of 12 fill weights from each machine yields sample mean and sample variance of X1 = 966.75, S21

= 29.30 from the first and X2 = 962.33, S22

= 26.24 from the second.

(a) State the null and alternative hypotheses. Is the test statistic in (9.2.14) appropriate for this data? Justify your answer.

(b) Test, at level α = 0.05, the hypotheses stated in part

(a) in two ways, once using the statistic in (9.2.14), and once using the statistic in (9.2.15). Report the p-values from each procedure. What assumptions, if any, are needed for the validity of this test procedure?

(c) Construct a 95% CI for the difference in the two means. Explain how the testing problem in

(a) can be conducted in terms of the CI, and check if the test result remains the same.