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Two machines are used for filling plastic bottles with a net volume of 16.0 ounc

ID: 2960075 • Letter: T

Question

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 sigma1 = 0.020 and sigma2 = 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. Do you think the engineer is correct? Use alpha = 0.05. What is the P-value for this test? Calculate a 95% confidence interval on the difference in means. Provide a practical interpretation of this interval. What is the power of the test in part (a) for a true difference in means of 0.04? Assuming equal sample sizes, what sample size should be used to assure that beta = 0.05 if the true difference in means is 0.04? Assume that alpha = 0.05.

Explanation / Answer

Group Machine 1 Machine 2
Mean 16.0150 16.0050
SD 0.0303 0.0255
SEM 0.0096 0.0081
N 10 10

(a) The test hypothesis is
Ho:1=2
Ha:1 not equal to 2

The test statistic is

t=(xbar1-xbar2)/[s1^2/n1 + s2^2/n2]

=(16.015-16.005)/sqrt(0.0303^2/10 + 0.0255^2/10)

= 0.798

The two-tailed P value equals 0.4347

Since p-value is larger than a=0.025, we do not reject Ho

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(b) Confidence interval:
  The mean of Machine 1 minus Machine 2 equals 0.0100
  95% confidence interval of this difference: From -0.0163 to 0.0363

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