Two machines are used to fill plastic bottles with dishwashing detergent. The standard deviations of fill volume are known to be σ1 = 0.10 fluid ounces and μ2 = 0.15 fluid ounces for the two machines, respectively. Two random samples of n1 = 12 bottles from machine 1 and n2 = 10 bottles from machine 2 are selected, and the sample mean fill volumes are σ30.87 fluid ounces and – 30.68 fluid ounces.
Assume normality.
(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).
(c) Construct a 95% upper-confidence interval on the mean difference in fill volume. Interpret this interval.