(a) Construct a 90% two-sided confidence interval on the mean difference in fill volume. (b) Construct a 95% two-sided confidence interval on the mean difference in fill volume. Compare 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
Two machines are used to fill plastic bottles with dishwashing detergent. The standard deviations of fill volume are known to be SD1= 0.11 fluid ounces and SD2=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 Xbar1=30.89 fluid ounces and Xbar2=30.67 fluid ounces. Assume normality.
(a) Construct a 90% two-sided confidence interval on the mean difference in fill volume.
(b) Construct a 95% two-sided confidence interval on the mean difference in fill volume. Compare 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.
(d) Test the hypothesis that both machines fill to the same mean volume. Use alpha=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 alpha=0.05 .
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