Two machines are used to fill plastic bottles with dishwashing detergent. Two random samples of "1 = 12 bottles from machine 1 and n2 = 10 bottles from machine 2 are selected, and the sample mean and the sample standard deviation fill volumes of machine 1, respectively, are X1 = 30.87 and Si = 0.1 fluid ounces. And the sample mean and the sample standard deviation fill volumes of machine 2, respectively, are X2 = 30.68 and S2 = 0.2 fluid ounces. Assume normality of the fill volumes of both machines. a) Construct a 90% two-sided confidence interval on the mean difference in fill volume. Interpret this interval. (b) Construct a 95% two-sided confidence interval on the mean difference in fill volume. Compare and comment on the width of this interval to the width of the interval in part (a).