When X1, X2,, Xn are independent Poisson variables,each with parameter m, and n is
Chapter 8, Problem 71(choose chapter or problem)
When X1, X2,, Xn are independent Poisson variables,each with parameter m, and n is large, the sample meanX has approximately a normal distribution with m 5 E(X)and V(X) 5 myn. This implies thatZ 5 X 2 mmynhas approximately a standard normal distribution. Fortesting H0: m 5 m0, we can replace m by m0 in the equationfor Z to obtain a test statistic. This statistic is actuallypreferred to the large-sample statistic with denominatorSyn (when the Xis are Poisson) because it is tailoredexplicitly to the Poisson assumption. If the number ofrequests for consulting received by a certain statisticianduring a 5-day work week has a Poisson distribution andthe total number of consulting requests during a 36-weekperiod is 160, does this suggest that the true average numberof weekly requests exceeds 4.0? Test using a 5 .02.
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