Adataanalystassumesthatthe n independentobservationsinadatafilecomefromaPoisson distribution. (a) Derivethelikelihood-ratiostatisticfortesting H0: = 0 against Ha: 0. (b) Simulatetheexactdistributionoftheteststatisticin(a)for

Adataanalystassumesthatthe n independentobservationsinadatafilecomefromaPoisson distribution.

(a) Derivethelikelihood-ratiostatisticfortesting H0: μ = μ0 against Ha: μ ≠ μ0.

(b) Simulatetheexactdistributionoftheteststatisticin(a)for n = 25, when μ0 = 3.0.

(Section A.5.2 of the R Appendixshowscodetodothis.)Comparegraphicallytothe limiting chi-squareddistribution.

(c) For n = 25, suppose y = 4.0. Findthe95%confidenceinterval for μ based onlikelihood-

ratio tests.

(d) Derive the likelihood-ratiotestof H0: μ1 = μ2 for independentPoissonsamplesofsizes n1 and n2.