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6.4.18. An experimenter takes a sample of size 1 from the Poisson probability model, pX (k) = e−λλk/k!, k = 0, 1, 2, . . . , and wishes to test H0: λ=6 versus H1:λ<6 by rejecting H0 if k ≤2. (a) Calculate the probability of committing a Type I error.

Can someone explain what is the best way to approach this problem thank you

Brian M. Scott
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Jelizabeth
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  • The best way to approach this problem is to first check the definition of Type 1 error in your textbook and to try to locate in your specific setting every quantity involved in this definition. What is a problem in this suggestion? – Did Mar 13 '13 at 23:06

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We make a Type I error if we wrongly reject the null hypothesis. So you need to calculate the probability that we get $0$ or $1$ or $2$ "successes" given that $\lambda=6$, that is, given that the null hypothesis holds.

You have a relevant formula. If $\lambda=6$, then the probability that $X=k$ is $e^{-6}\dfrac{6^k}{k!}$. You need to calculate $\Pr(X=0)+\Pr(X=1)+\Pr(X=2)$. Approximations by the normal are not appropriate.

André Nicolas
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