The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. The following sample data show the weight of bags (in pounds) produced on two machines: machine 1 and 2.
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 for each model; in particular, the sample variance and the sample size for each machine.
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b) Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for two 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 critical values 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 to confirm your results above are correct.
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h) Construct a 95% confidence interval for the variance of the weight of bags produced on machine 1.
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i) Construct a 95% confidence interval for the standard deviation of the weight of bags produced on machine 2.
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j) Which machine, if either, provides the greater opportunity for quality improvements?