Refer to Exercise 7. Someone suggests that the paired design be replaced with a design in which

Question:

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.

Refer to Exercise 7

For a sample of nine automobiles, the mileage (in 1000s of miles) at which the original front brake pads were worn to 10% of their original thickness was measured, as was the mileage at which the original rear brake pads were worn to 10% of their original thickness. The results are given in the following table.