Two machines are used for filling plastic bottles with a netvolume of 16.0 ounces. The filling processes can be assumed tobe normal, with standard deviation of1 = 0.015 and2 = 0.018. The quality engineeringdepartment suspects that both machines fill to the same net volume, whether or not this volume is 16.0 ounces. An experiment isperformed by taking a random sample from the output of eachmachine.
Machine 1

Machine 2

16.03

16.01

16.02

16.03

16.04

15.96

15.97

16.04

16.05

15.98

15.96

16.02

16.05

16.02

16.01

16.01

16.02

15.99

15.99

16.00

(a) State the hypotheses that should be tested in thisexperiment

(b) Test thesehypotheses using =0.05. What are yourconclusions?

(c) What is theP-value for the test? P = 0.1770

(d) Find a 95percent confidence interval on the difference in the mean fillvolume for the two machines.