Suppose that the number of defects in a piece of wire of length t yards is Poisson distributed, X ~ POI(lambda *t), and one defect is found in a 100 - yard piece of wire.
a) Test Ho: lambda > or = to .05 against Ha: lambda < .05 with significance level at most .01.
b) What is the p-value for such a test?
c) Suppose a total of two defects are found in two 100-yard pieces of wire. Test Ho: lambda > or = to .05 versus Ha: lambda < .05 at significance level alpha = .0103.
d) Find the power of the test in c) if lambda = .01.