Question: A quality-control engineer wants to find out whether or not a new machine that fills bottles with liquid has a different average filling content than of the machine currently in use. The engineer calibrates each machine to fill bottles with 16 ounces of liquid. After running each machine for five hours, she randomly selects 15 filled bottles from each machine and measures their contents. The Filling Machines data is given with this test. You would like to construct a 95% confidence interval of the mean difference in filling contents between the two machines. (Do all steps regardless of your conclusions when doing Part (b))

(a) (2 points) State the appropriate statistical procedure.

(b) (2 points) Check the assumption that the sample sizes from both groups are large enough or the data from both groups are normally distributed. (If graphs are needed, print these outputs from EXCEL and interpret)

(c) (2 points) What descriptive statistics would you use to describe the data (both numerical and graphical)? Please show the descriptive statistics (paste the correct graphic as part of your answer).

(d) (2 points) Determine the Degrees of freedom for this analysis.

(e) (2 points) Calculate and interpret the 95% Confidence Interval of the difference in mean difference in filling content between the two machines.

(f) (2 points) Do you think there is a mean difference in filling content between the two machines after creating the confidence interval? Why?