Two machines are used to fill plastic bottles with dishwashing detergent. The standard deviations of fill volume are known to be s₁ = 0.10 fluid ounces and s₂ = 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 1= 30.94 fluid ounces and 2 = 30.56 fluid ounces. Assume normality. (Express the results to 4 significant digits.)
a) Calculate a 90% two-sided confidence interval on the mean difference in fill volume.