Refer to Exercise 7. Someone suggests that the paired design be replaced with a design in which 18 cars are sampled, the lifetime of the front brakes is measured on 9 of them, and the lifetime of the rear brakes is measured on the other 9. A confidence interval for the difference between the means would then be constructed by using expression (5.21) (in Section 5.6). He claims that this design will produce a more precise confidence interval, since 18 cars will be used instead of 9.
a. Will the new design produce a valid confidence interval? Explain.
b. Is it likely that the confidence interval produced by the new design will be more precise than, less precise than, or about equally precise as the confidence interval produced by the paired design? Explain.
(a) Yes. This design involves two independent samples, so a confidence interval for the difference between the two means can be constructed by using expression (5.21) in Section 5.6.
(b) It is likely to be less precise, because there is likely to be a lot of variation in brake pad life from one car to another.
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