Two machines are used for filling plastic bottles with a net volume of 16.0 ounces. The fill volume can be assumed to be normal with standard deviation σ₁= 0.020 and σ₂= 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.

(a) Do you think the engineer is correct? Use α = 0.05. What is the P-value for this test?

(b) Calculate a 95% confidence interval on the difference in means. Provide a practical interpretation of this interval.

(c) What is the power of the test in part (a) for a true difference in means of 0.04?

(d) Assume that sample sizes are equal. What sample size should be used to ensure that β = 0.05 if the true difference in means is 0.04? Assume that α = 0.05.

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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