Two machines are used for filling plastic bottles with a net volume of 16.0 ounces. The fill volume can be assumed normal, with standard deviation o1 = 0.020 and o2 = 0.025 ounces. A member of the quality engineering staff suspects that both machines fill to the same mean net volume, whether or not this volume is 16.0 ounces. A random sample of 10 bottles is taken from the output of each machine. MACHINE 1 MACHINE 2 16.03 16.01 16.02 16.03 16.04 15.96 15.97 16.04 16.05 15.98 15.96 16.02 16.05 16.02 16.01 16.01 16.02 15.99 15.99 16.00 (a) Do you think the engineer is correct? Use a = 0.05. (b) What is the P-value for this test? (c) What is the power of the test in part (a) for a true difference in means of 0.04? (d) Find a 95% confidence interval on the difference in means. Provide a practical interpretation of this interval. (e) Assuming equal sample sizes, what sample size should be used to assure that ß = 0.05 if the true difference in means is 0.04? Assume that a = 0.05.
Two machines are used for filling plastic bottles with a net volume of 16.0 ounces. The fill volume can be assumed normal, with standard deviation o1 = 0.020 and o2 = 0.025 ounces. A member of the quality engineering staff suspects that both machines fill to the same mean net volume, whether or not this volume is 16.0 ounces. A random sample of 10 bottles is taken from the output of each machine. MACHINE 1 MACHINE 2 16.03 16.01 16.02 16.03 16.04 15.96 15.97 16.04 16.05 15.98 15.96 16.02 16.05 16.02 16.01 16.01 16.02 15.99 15.99 16.00 (a) Do you think the engineer is correct? Use a = 0.05. (b) What is the P-value for this test? (c) What is the power of the test in part (a) for a true difference in means of 0.04? (d) Find a 95% confidence interval on the difference in means. Provide a practical interpretation of this interval. (e) Assuming equal sample sizes, what sample size should be used to assure that ß = 0.05 if the true difference in means is 0.04? Assume that a = 0.05.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Two machines are used for filling plastic bottles with a net volume of 16.0 ounces. The fill volume can be
assumed normal, with standard deviation o1 = 0.020 and o2 = 0.025 ounces. A member of the quality
engineering staff suspects that both machines fill to the same mean net volume, whether or not this volume
is 16.0 ounces. A random sample of 10 bottles is taken from the output of each machine.
MACHINE 1
MACHINE 2
16.01
16.02
16.03
16.03
16.04
15.96
15.97
16.04
16.05
15.98
15.96
16.02
16.05
16.02
16.01
16.01
16.02
15.99
15.99
16.00
(a) Do you think the engineer is correct? Use a = 0.05.
(b) What is the P-value for this test?
(c) What is the power of the test in part (a) for a true difference in means of 0.04?
(d) Find a 95% confidence interval on the difference in means. Provide a practical interpretation of
this interval.
(e) Assuming equal sample sizes, what sample size should be used to assure that ß = 0.05 if the
true difference in means is 0.04? Assume that a = 0.05.
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