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

Chapter 5, Problem 8

(choose chapter or problem)

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.

Will the new design produce a valid confidence interval? Explain. 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. (Hint: Look at Figure 5.15.)