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 a sample mean and variance of 986.75 and 27.3, re- spectively, from the first machine, and 992.33 and 26.24, respectively, from the second machine.

a) State the null and alternative hypotheses. What assumptions, if any, are necessary to conduct a valid test?

b) Test, at level = 0.05, the hypotheses stated in part (a). Report the p- value. Explain your choice of test statistic.

c) Construct a 90% CI for the difference in the two means.