Two machines are used to fill plastic bottles with dishwashing detergent. The standard

Chapter 10, Problem 10-85

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Two machines are used to fill plastic bottles with dishwashing detergent. The standard deviations of fill volume are known to be 1 0.10 fluid ounces and 2 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 30.87 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. (d) Test the hypothesis that both machines fill to the same mean volume. Use 0.05. What is the P-value? (e) If the -error of the test when the true difference in fill volume is 0.2 fluid ounces should not exceed 0.1, what sample sizes must be used? Use 0.05.