2. The cloth produced by a certain manufacturer has defects that occur randomly at a constant rate of \(\lambda\) per square metre. If \(\lambda\) is thought to be greater than 1.5 then action has to be taken. Using \(\mathrm { H } _ { 0 } : \lambda = 1.5\) and \(\mathrm { H } _ { 1 } : \lambda > 1.5\) a quality control officer takes a \(4 \mathrm {~m} ^ { 2 }\) sample of cloth and rejects \(\mathrm { H } _ { 0 }\) if there are 11 or more defects. If there are 8 or fewer defects she accepts \(\mathrm { H } _ { 0 }\). If there are 9 or 10 defects a second sample of \(4 \mathrm {~m} ^ { 2 }\) is taken and \(\mathrm { H } _ { 0 }\) is rejected if there are 11 or more defects in this second sample, otherwise it is accepted.

1. Find the size of this test.
2. Find the power of this test when \(\lambda = 2\)