The variance in a production process is an important measure ofthe quality of the process. A large variance often signals anopportunity for improvement in the process by finding ways toreduce the process variance. The following sample data show theweight of bags (in pounds) produced on two machines: machine 1 and2.

m1 = (2.95, 3.45, 3.50, 3.75, 3.48,3.26, 3.33, 3.20, 3.16, 3.20, 3.22, 3.38, 3.90, 3.36, 3.25, 3.28,3.20, 3.22, 2.98, 3.45, 3.70, 3.34, 3.18, 3.35, 3.12)

m2 = (3.22, 3.30, 3.34, 3.28, 3.29,3.25, 3.30, 3.27, 3.38, 3.34, 3.35, 3.19, 3.35, 3.05, 3.36, 3.28,3.30, 3.28, 3.30, 3.20, 3.16, 3.33)

A) Provide descriptive statistical summaries of the data foreach model; in particular, the sample variance and the sample sizefor each machine.

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B) Conduct a statistical test to determine whether there is asignificant difference between the variances in the bag weights fortwo machines. First, clearly formulating your hypotheses below.

C) Compute the test statistic.

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D) Compute the p value.

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E) Use a .05 level of significance to compute both criticalvalues for your test statistic.

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F) Use a .05 level of significance. What is your conclusion?

G) Use the function var.test() in R to run the test directly toconfirm your results above are correct.

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H) Construct a 95% confidence interval for thevariance of the weight of bags produced on machine1.

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I) Construct a 95% confidence interval for the standarddeviation of the weight of bags produced on machine 2.

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J) Which machine, if either, provides the greater opportunityfor quality improvements?