10. Inference about the ratio of two variances Label Check is a consulting firm that works with food manufacturers to verify the nutritional information on their product labels. Label Check needs to decide whether to award a contract to Laboratory A or Laboratory B to conduct some of its food testing. If there is a significant difference in the reliability of the two labs, the contract will be awarded to the lab that is more reliable. Allpurpose egg mix is a dried egg mixture that can be reconstituted with water and used in recipes that call for eggs. According to the package label, each twotablespoon serving of egg mix contains 6 grams of protein. Label Check's managers use the variance of a lab's measurements as an Indicator of the labs reliability. To compare the reliability of the two labs, Label Check extracts 24 twotablespoon samples from a wellmixed container of dried egg mix, sending 12 samples to Lab A and 12 to Lab B. The labs are instructed to measure the protein content in each of their 12 samples and report their results to Label Check. Sample A (the 12 measurements from Lab A) and sample B (the 12 measurements from Lab B) are independent, random samples. It is safe to assume that the populations from which the samples are drawn are normally distributed. Sample A has a sample mean of 6.032 and a sample variance of 0.178; sample B has a sample mean of 5.968 and a sample variance of 0.050. Label Check uses the sample statistics to conduct a two tai'l hypothesis test of the equality of the two population variances. Let's designate the population from which Lab A's measurements are drawn as population 1 and the population from which Lab B's measurements are drawn as population 2. The value of the test statistic is Y Select a Distribution Distributions 0 1 2 3 Label Check conducts its hypothesis test using a level of significance of a = 0.05. Use the Distributions tool to develop the rejection region. According to the critical value approach, you: O Reject Ho if F 2 2.818 O Reject Ho if F