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2.6 Second-curtain sync can produce interesting effects when you use a stationary camera as in this shot of David Lutz, photographer, and a passing freight train. Taken in Manual mode at ISO 1600, f/6.3, 1/60 second with a 6.1mm lens setting.

10-1 Two machines are used for lling plastic bottles with a net volume of 160 ounces The ll volume can be assumed normal, with standard deviation 1 0020 and 2 0025 ounces A member of the quality engineering staff suspects that both machines ll to the same mean net volume, whether or not this volume is 160 ounces A random sample of 10 bottles is taken from the output of each machine Machine 1 1603 1604 1605 1605 1602 1601 1596 1598 1602 1599 Machine 2 1602 1597 1596 1601 1599 1603 1604 1602 1601 1600 20 specimens are tested; the sample mean burnand n2 ing rates are x1 18 centimeters per second and x2 24 centimeters per second.

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(a) Test the hypothesis that both propellants have the same mean burning rate Use 005 (b) What is the P-value of the test in part (a) (c) What is the -error of the test in part (a) if the true difference in mean burning rate is 25 centimeters per second (d) Construct a 95% con dence interval on the difference in means 1 2 What is the practical meaning of this interval 10-5 Two machines are used to ll plastic bottles with dishwashing detergent The standard deviations of ll volume are known to be 1 010 uid ounces and 2 015 uid 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 ll volumes are x1 3087 uid ounces and x2 3068 uid ounces.

5 5 21 10 37 4 53 3

Assume normality (a) Construct a 90% two-sided con dence interval on the mean difference in ll volume Interpret this interval (b) Construct a 95% two-sided con dence interval on the mean difference in ll volume Compare and comment on the width of this interval to the width of the interval in part (a) (c) Construct a 95% upper-con dence interval on the mean difference in ll volume Interpret this interval 10-6 Reconsider the situation described in Exercise 10-5 (a) Test the hypothesis that both machines ll to the same mean volume Use 005 (b) What is the P-value of the test in part (a) (c) If the -error of the test when the true difference in ll volume is 02 uid ounces should not exceed 01, what sample sizes must be used Use 005 10-7.

Two different formulations of an oxygenated motor fuel are being tested to study their road octane numbers The variance of road octane number for formulation 1 is 2 15, and for 1 2 formulation 2 it is 2 12 Two random samples of size n1 15 and n2 20 are tested, and the mean road octane numbers observed are x1 896 and x2 925 Assume normality (a) Construct a 95% two-sided con dence interval on the difference in mean road octane number (b) If formulation 2 produces a higher road octane number than formulation 1, the manufacturer would like to detect.

6 6 22 15 38 7 54 10

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