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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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$## Exercises on Statistical Testing ### 16. An experimenter drew random samples from two normal distributions with different means but the same variance. The first sample contained 18 independent observations, and the second contained 11. The sample variances were $ S_1^2 = 92 $ for the first sample and $ S_2^2 = 86 $ for the second. What are the 99% confidence limits for the variance of either population? ### 17. Suppose that the experimenter in Exercise 15 had taken both a sample of 25 six-year-old children and a similar sample of nine-year-old children. The variance for the six-year-olds was $ S^2 = 945 $, while for the nine-year-olds, it was $ S^2 = 919 $. Is it reasonable to conclude that six-year-olds are more variable than nine-year-olds? Use $ \alpha = 0.05 $. ### 18. The test carried out in Exercise 17, Chapter 8, involves the assumption that the two populations have exactly the same variance. Test this assumption using $ \alpha = 0.01 $. ### 19. Using the two samples in Exercise 21, Chapter 8, test the hypothesis that the two populations have the same variance against the alternative that the variance for Population I is greater. Use $ \alpha = 0.05 $. ### 20. Use the data in Exercise 20, Chapter 8, to test the hypothesis that the two brands of gasoline have the same variance in terms of mileage, against the hypothesis that Brand I is more variable. The 0.05 level for $ \alpha $ may be used. ### 21. Two normally distributed populations are being compared to see if they have the same values for their variances. The alternative hypothesis is that Population I has the larger variance. A sample of 13 independent observations are drawn from Population 1 and a separate random sample of nine observations are made of Population 2. Sample 1 had $ S_1^2 = 141 $, and Sample 2 shows $ S_2^2 = 123 $. What can one conclude about the variances of the two populations? ### 22. Suppose that independent random samples each consisting of 16 cases were drawn at random from two normal populations. The first sample produced a sample standard deviation $ S = 38.2 $$

Transcribed Image Text:## Exercises on Statistical Testing ### 16. An experimenter drew random samples from two normal distributions with different means but the same variance. The first sample contained 18 independent observations, and the second contained 11. The sample variances were $ S_1^2 = 92 $ for the first sample and $ S_2^2 = 86 $ for the second. What are the 99% confidence limits for the variance of either population? ### 17. Suppose that the experimenter in Exercise 15 had taken both a sample of 25 six-year-old children and a similar sample of nine-year-old children. The variance for the six-year-olds was $ S^2 = 945 $, while for the nine-year-olds, it was $ S^2 = 919 $. Is it reasonable to conclude that six-year-olds are more variable than nine-year-olds? Use $ \alpha = 0.05 $. ### 18. The test carried out in Exercise 17, Chapter 8, involves the assumption that the two populations have exactly the same variance. Test this assumption using $ \alpha = 0.01 $. ### 19. Using the two samples in Exercise 21, Chapter 8, test the hypothesis that the two populations have the same variance against the alternative that the variance for Population I is greater. Use $ \alpha = 0.05 $. ### 20. Use the data in Exercise 20, Chapter 8, to test the hypothesis that the two brands of gasoline have the same variance in terms of mileage, against the hypothesis that Brand I is more variable. The 0.05 level for $ \alpha $ may be used. ### 21. Two normally distributed populations are being compared to see if they have the same values for their variances. The alternative hypothesis is that Population I has the larger variance. A sample of 13 independent observations are drawn from Population 1 and a separate random sample of nine observations are made of Population 2. Sample 1 had $ S_1^2 = 141 $, and Sample 2 shows $ S_2^2 = 123 $. What can one conclude about the variances of the two populations? ### 22. Suppose that independent random samples each consisting of 16 cases were drawn at random from two normal populations. The first sample produced a sample standard deviation $ S = 38.2 $

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