In commercial food service and manufacturing, consistency in the product is essential so that customers know exactly what they're getting every time they purchase a product. A liquor distillery has 37 barrels of a ten-year old batch. The quantity of the flavor compound vanillin is measured from each of the 37 barrels in parts per thousand (ppt): vanillin

a) First, review the hypothesis testing procedure. If there is too much variability in the batches, then customers won't get a consistent product, so the variance cannot exceed o2 = 10 ppt. We wish to test Ho : 02 = 10 vs. HA : 02 > 10. Let a = 0.05. Test your hypothesis with a one-sided confidence interval built with VarTest. Verify the confidence interval bounds by computing the values by hand. Fail to reject the null since 10 falls inside the confidence interval. b) Next test with a rejection region. Start by building a test statistic and stating the sampling distribution of the statistic under the null hypothesis. Verify the value of Xobs computed by VarTest. C) If the flavor is too strong or too weak, the batch must be rejected. The target is / = 42 ppt. Assume flavor levels are normally distributed and that the true variance is unknown. Test Ho : M = 42 ppt vs. HA : u # 45 ppt at significance level o = 0.01, two ways: 1) with a two-sided confidence interval and 2) with a two-sided rejection region. Verify each answer with t . test