#21 only SIA16. An experimenter drew random samples from two normal distributions, with different meansbut with the same variance. The first sample contained 18 independent observations, and the secondcontained 11. If the two sample variances turned out to be S = 92 for the first sample, and S₂ = 86for the second, what are the 99% confidence limits for the variance of either population?QUOISHob217. Suppose that the experimenter in Exercise 15 had taken both a sample of 25 6-year-oldchildren and a similar random sample of the same number of 9 year olds. The 6 year olds againshowed S² = 945, whereas the 9-year-old children had S² = 919. Is it reasonable to conclude that6 year olds are more variable than 9 year olds? Use α == .05.Exercises18. The test carried out in Exercise 17, Chapter 8, involves the assumption that the two popula-tions have exactly the same variance. Test this assumption using a = .01.19. Using the two samples in Exercise 21, Chapter 8, test the hypothesis that the two populationshave the same variance, against the alternative that the variance for Population I is greater. Againuse α = .05.21. Two normally distributed populations are being compared to see if they have the same valuesfor their variances. The alternative hypothesis is that Population 1 has the larger variance. A sampleof 13 independent observations are drawn from Population 1 and a separate random sample of nineindependent observations are made of Population 2. Sample 1 shows that S = 141, and Samplemor2 shows S2 = 123. What can one conclude about the variances of the two populations?COMENT20. Use the data in Exercise 20, Chapter 8, to test the hypothesis that the two brands of gasolinehave the same variance in terms of mileage, against the hypothesis that Brand I is the more variable.The .05 level for a may be used.37522. Suppose that independent random samples each consisting of 16 cases were drawn at randomfrom two normal populations. The first sample produced a sample standard deviation S = 38.2 andthe second sample a standard deviation S = 89.2. The null hypothesis was Ho: o = o2 and thealternative was "not Ho." Test the null hypothesis.tomuffroup23. Is it possible to test a hypothesis of the form Ho: o = ko2? Explain why it should or shouldnot be possible, and if possible, how one would go about doing so.Stayed FreshDid Not Stay Fresh24. A metropolitan bank advertises that the odds are 9 to 1 that a customer entering the lobbywill have his or her transaction completed in 5 minutes. An observer spent some time in the banklobby and observed a sample of 460 customers. It turned out that of this sample, some 400 actuallywere finished in 5 minutes. Treat this as a random sample of the population of bank customers, anduse the Pearson chi-square method to evaluate the goodness of fit between the advertising claimand the reality of the bank's operation. Use a = .05.bar ows vino 910QUOTE noroitibCATEY+0530won sigsilib25. Two rival baking companies put out the same variety of bran muffins. However, a consumeradvocacy organization suspected that the muffins from the two bakeries differed in their tendencyto stay fresh for longer than 1 day. To test this relationship between the source of a muffin andits tendency to stay fresh, a random sample of 2,400 muffins (1,200 from each bakery) was taken.The results in terms of numbers of muffins were as follows:Bakery A481719Bakery B69051001vilniboisioonnog odod bloode oals i jud,pigan?asana to agaiquorg ustunsupbetweUse the Pearson chi-square test of association to decide if there is evidence for association (a.05)

Question

#21 only SIA16. An experimenter drew random samples from two normal distributions, with different meansbut with the same variance. The first sample contained 18 independent observations, and the secondcontained 11. If the two sample variances turned out to be S = 92 for the first sample, and S₂ = 86for the second, what are the 99% confidence limits for the variance of either population?QUOISHob217. Suppose that the experimenter in Exercise 15 had taken both a sample of 25 6-year-oldchildren and a similar random sample of the same number of 9 year olds. The 6 year olds againshowed S² = 945, whereas the 9-year-old children had S² = 919. Is it reasonable to conclude that6 year olds are more variable than 9 year olds? Use α == .05.Exercises18. The test carried out in Exercise 17, Chapter 8, involves the assumption that the two popula-tions have exactly the same variance. Test this assumption using a = .01.19. Using the two samples in Exercise 21, Chapter 8, test the hypothesis that the two populationshave the same variance, against the alternative that the variance for Population I is greater. Againuse α = .05.21. Two normally distributed populations are being compared to see if they have the same valuesfor their variances. The alternative hypothesis is that Population 1 has the larger variance. A sampleof 13 independent observations are drawn from Population 1 and a separate random sample of nineindependent observations are made of Population 2. Sample 1 shows that S = 141, and Samplemor2 shows S2 = 123. What can one conclude about the variances of the two populations?COMENT20. Use the data in Exercise 20, Chapter 8, to test the hypothesis that the two brands of gasolinehave the same variance in terms of mileage, against the hypothesis that Brand I is the more variable.The .05 level for a may be used.37522. Suppose that independent random samples each consisting of 16 cases were drawn at randomfrom two normal populations. The first sample produced a sample standard deviation S = 38.2 andthe second sample a standard deviation S = 89.2. The null hypothesis was Ho: o = o2 and thealternative was &#34;not Ho.&#34; Test the null hypothesis.tomuffroup23. Is it possible to test a hypothesis of the form Ho: o = ko2? Explain why it should or shouldnot be possible, and if possible, how one would go about doing so.Stayed FreshDid Not Stay Fresh24. A metropolitan bank advertises that the odds are 9 to 1 that a customer entering the lobbywill have his or her transaction completed in 5 minutes. An observer spent some time in the banklobby and observed a sample of 460 customers. It turned out that of this sample, some 400 actuallywere finished in 5 minutes. Treat this as a random sample of the population of bank customers, anduse the Pearson chi-square method to evaluate the goodness of fit between the advertising claimand the reality of the bank's operation. Use a = .05.bar ows vino 910QUOTE noroitibCATEY+0530won sigsilib25. Two rival baking companies put out the same variety of bran muffins. However, a consumeradvocacy organization suspected that the muffins from the two bakeries differed in their tendencyto stay fresh for longer than 1 day. To test this relationship between the source of a muffin andits tendency to stay fresh, a random sample of 2,400 muffins (1,200 from each bakery) was taken.The results in terms of numbers of muffins were as follows:Bakery A481719Bakery B69051001vilniboisioonnog odod bloode oals i jud,pigan?asana to agaiquorg ustunsupbetweUse the Pearson chi-square test of association to decide if there is evidence for association (a.05)

Accepted Answer

Given that 
Sample size n1=13 , n2=9
Sample variance s12=141 , s22=123