Two machines are used to fill plastic bottles with dishwashing detergent. The standard deviations of fill volume are known to be 3 ml and 4 ml for the two machines, respectively. Two random samples of 12 bottles from machine 1 and 10 bottles from machine 2 are selected, and the mean fill volumes are 905 and 897 ml. Assume normality, (a) Test the hypothesis that both machines fill to the same mean volume, use P-value approach, (b) What sample size must be used to maintain the type I error at 0.05 and type II error at 0.10 for a true difference in fill volume of 6 ml? (c) Construct a 90% CI on the mean difference in fill volume and interpret this interval.