Determine the following:  Do you think the engineer is correct? Use α = 0.05. What is the P-value for this test? What is the power of the test in part (a) for a true difference in means of 0.04?  Find a 95% confidence interval on the difference in means. Provide a practical interpretation of this interval. Assuming equal sample sizes, what sample

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Chapter1: Combinatorial Analysis
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Determine the following: 

  • Do you think the engineer is correct? Use α = 0.05.
  • What is the P-value for this test?
  • What is the power of the test in part (a) for a true difference in means of 0.04? 
  • Find a 95% confidence interval on the difference in means. Provide a practical interpretation of this interval.
  • Assuming equal sample sizes, what sample size should be used to assure that β = 0.05 if the true difference in means is 0.04? Assume that α = 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. .
МАCHINE 1
МАCHINE 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
Transcribed Image Text: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. . МАCHINE 1 МАCHINE 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
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With the same given above, can you please answer the remaining two questions below?

  • Find a 95% confidence interval on the difference in means. Provide a practical interpretation of this interval.
  • Assuming equal sample sizes, what sample size should be used to assure that β = 0.05 if the true difference in means is 0.04? Assume that α = 0.05.

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