$5-66.$ Two different types of injection$-$molding machines

are used to form plastic parts. A part is considered defective if

it has excessive shrinkage or is discolored. Two random sam$-$

ples, each of size $400,$ are selected, and $20$ defective parts are

found in the sample from machine $1$ whereas $10$ defective parts

are found in the sample from machine $2.$ Is it reasonable to

conclude that both machines produce the same fraction of de$-$

fective parts, using $=0\mathrm{.}05?$ Find the $P-$value for this test.