Question 3 3. We get two random samples from two normal populations. The first sample yields 5.5, 8.7, 6.8, 8.9, 7.9, 8.5, and the second sample yields

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Question 3
3. We get two random samples from two normal populations. The first sample yields
5.5, 8.7, 6.8, 8.9, 7.9, 8.5,
and the second sample yields
15.8, 14.3, 17.9,
15.6, 14.7.
(a) Construct a 99% confidence interval for the ratio of the two population variances if
(i) you have no information on the two population means
(ii) you know that the mean of the first population is 8.5
(iii) you know that the first mean is 8.5 and the second mean is equal to 15.5
(b) Compare, and interpret the results you have obtained. In particular, in which of these three different cases can you
conclude that the two variances are equal? Carefully describe your reasoning.
Transcribed Image Text:4 of 5 Question 3 3. We get two random samples from two normal populations. The first sample yields 5.5, 8.7, 6.8, 8.9, 7.9, 8.5, and the second sample yields 15.8, 14.3, 17.9, 15.6, 14.7. (a) Construct a 99% confidence interval for the ratio of the two population variances if (i) you have no information on the two population means (ii) you know that the mean of the first population is 8.5 (iii) you know that the first mean is 8.5 and the second mean is equal to 15.5 (b) Compare, and interpret the results you have obtained. In particular, in which of these three different cases can you conclude that the two variances are equal? Carefully describe your reasoning.
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