Self$-$Review $18-4$ The assembly area of Gotrac Products was recently redesigned. Installing a new lighting

system and purchasing new workbenches were two features of the redesign. The produc$-$

tion supervisor would like to know if the changes resulted in an improvement in worker

productivity. To investigate, she selected a sample of $11$ workers and determined the

production rate before and after the changes. The sample information is reported below.

$($a$)$ How many usable pairs are there? That is$,$ what is $n?$

$($b$)$ Use the Wilcoxon signed$-$rank test to determine whether the new procedures actually

increased production. Use the $\mathrm{.}05$ level and a one$-$tailed test.

$($c$)$ What assumption are you making about the distribution of the differences in production

before and after redesign?