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. Then, he claims that this design will produce a more precise confidence interval, since 18 cars will be used instead of 9. Required:
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.