The sum of the values obtained in a random sampleof size n = 5 is to be used to test the null hypothesisthat on the average there are more than two accidents perweek at a certain intersection (that λ > 2 for this Poissonpopulation) against the alternative hypothesis that on theaverage the number of accidents is two or less. If the nullhypothesis is to be rejected if and only if the sum of theobservations is five or less, find(a) the probabilities of type I errors when λ = 2.2, 2.4, 2.6,2.8, and 3.0;(b) the probabilities of type II errors when λ = 2.0, 1.5,1.0, and 0.5.Also, plot the graph of the power function of this testcriterion.

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