5. Inference about the ratio of two variances Aa Aa Label Check is a consulting

Question

5. Inference about the ratio of two variances Aa Aa 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. All-purpose 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 two-tablespoon serving of egg mix contains 6 grams of proteirn, Label Check's managers use the variance of a lab's measurements as an indicator of the lab's reliability. To compare the reliability of the two labs, Label Check extracts 24 two-tablespoon samples from a well-mixed 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 0.162; 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-tail 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

Explanation / Answer

here test statistic F =(s1/s2)2 =(0.162/0.050) =3.24

at (n1-1=11) and (n2-1=11) degree of freedom and 0.05 level rejection region:

reject Ho if F<=0.288 or if F>=3.474

p value =0.0635

the null hypothsis of equal population variances is not rejected so label check will have equal variance

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.