$3)$ An electrical engineer must design a circuit to deliver the maximum amount of current to a display tube to achieve su$$cient image brightness. Within her allowable design constraints, she has developed two candidate circuits and tests

Delta: $13,10,1,4,0,9($minutes late$)$

Alaska: $15,8,3,1,2,4($minutes late$)$

The manufacturer of a hot tub is interested to test prototypes of each. The resulting data $($in microamperes$)$ are as follows:

Circuit $1$: $251,255,258,257,250,251,254,250,248$

Circuit $2$: $250,253,249,256,259,252,260,251$

a$.$ Use the Wilcoxon rank$-$sum test to test H$0$: $\backslash$mu $1=\backslash$mu $2$ against the alternative H$1$: $\backslash$mu $1>\backslash$mu $2.$ Use $\backslash$alpha $=0\mathrm{.}025.$

b$.$ Use the normal approximation for the Wilcoxon rank$-$ sum test. Assume that $\backslash$alpha $=0\mathrm{.}05.$ Find the approximate P$-$value for this test statistic.