Two machines are used for filling plastic bottles with a net volume of 16.0 ounces. the fill volume can be assumed normal, with standard deviation 01 = 0.020 and 02 = 0.025 ounces. a member of the quality engineering staff suspects that bothmachines fill to the same mean net volume, whether or not this volume is 16.0 ounces. a random sample of 10 bottles istaken from the output of each machine.16.03 16.01 16.02 16.0316.04 15.96 15.97 16.0416.05 15.98 15.96 16.0216.05 16.02 16.01 16.0116.02 15.99 15.99 16.00(a) do you think the engineer is correct? use the p-value approach.(b) if a = 0.05, what is the power of the test in part (a) for a true difference in means of 0.04? (c) find a 95% cl on the difference in means. provide a practical interpretation of this interval.(d) assuming equal sample sizes, what sample size should be used to ensure that b = 0.01 ifthe true difference in means is0.04? assume that a = 0.05.