(b) Tests were made to determine the performance of cars in kilometres per litre of petrol using two additives. Eighteen new vehicles of the same type took part, nine using additive 1, and the other 9 using additive 2. The average distance covered by each car per litre is given in the table below. You are given that the average distances are normally distributed. Additive 1 12.3 17.3 15.5 13.7 11.9 10 14.6 12.8 16.4 Additive 2 18.4 14.8 16.6 12 13.9 15.7 17.5 16.3 14.3 (i) State an appropriate pivotal quantity for estimating, the ratio of the population variances. (ii) Derive a 100(1-a) % confidence interval for, the ratio of the population variances. (iii) Construct a 99% confidence interval for, the ratio of the population variances.
(b) Tests were made to determine the performance of cars in kilometres per litre of petrol using two additives. Eighteen new vehicles of the same type took part, nine using additive 1, and the other 9 using additive 2. The average distance covered by each car per litre is given in the table below. You are given that the average distances are normally distributed. Additive 1 12.3 17.3 15.5 13.7 11.9 10 14.6 12.8 16.4 Additive 2 18.4 14.8 16.6 12 13.9 15.7 17.5 16.3 14.3 (i) State an appropriate pivotal quantity for estimating, the ratio of the population variances. (ii) Derive a 100(1-a) % confidence interval for, the ratio of the population variances. (iii) Construct a 99% confidence interval for, the ratio of the population variances.
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.
Chapter7: Integration
Section7.CR: Chapter 7 Review
Problem 88CR
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Transcribed Image Text:(b) Tests were made to determine the performance of cars in kilometres per litre of
petrol using two additives. Eighteen new vehicles of the same type took part,
nine using additive 1, and the other 9 using additive 2. The average distance
covered by each car per litre is given in the table below. You are given that the
average distances are normally distributed.
Additive 1 12.3 17.3 15.5 13.7 11.9 10 14.6 12.8 16.4
Additive 2 18.4 14.8 16.6 12 13.9 15.7 17.5 16.3 14.3
(i) State an appropriate pivotal quantity for estimating the ratio of the
population variances.
(ii) Derive a 100(1-a)% confidence interval for, the ratio of the population
variances.
(iii) Construct a 99% confidence interval for, the ratio of the population
variances.
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