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From: rabbits77 on 21 Feb 2010 16:34
X_1,...,X_8 are a random sample of
size n=8 from a poisson distribution with mean m.
Reject the simple null hypothesis Ho: m=0.5
and accept H_1: m > 0.5 if the observed sum

\Sum_{i=1}^8 x_i >=8.

How do I calculate the significance level
alpha of this test?
From: rabbits77 on 21 Feb 2010 18:53
rabbits77 wrote:
> X_1,...,X_8 are a random sample of
> size n=8 from a poisson distribution with mean m.
> Reject the simple null hypothesis Ho: m=0.5
> and accept H_1: m > 0.5 if the observed sum
>
> \Sum_{i=1}^8 x_i >=8.
>
> How do I calculate the significance level
> alpha of this test?
I think I am on a correct path for this...
This is to computed the same as
P(X >= 8) = 1 - P(X <= 7)
and for a poisson distribution
with m=0.5 and x = 7 that is
1 - 1 = 0.
Hmmm, that looks odd. Am I right or did I
do this incorrectly? Where did I go wrong?

From: Ray Vickson on 21 Feb 2010 20:39
On Feb 21, 1:34 pm, rabbits77 <rabbit...(a)my-deja.com> wrote:
> X_1,...,X_8 are a random sample of
> size n=8 from a poisson distribution with mean m.
> Reject the simple null hypothesis Ho: m=0.5
> and accept H_1: m > 0.5 if the observed sum
>
> \Sum_{i=1}^8 x_i >=8.
>
> How do I calculate the significance level
> alpha of this test?

Assuming m = 0.5 is true, the distribution of X = sum_{i=1}^8 X_i is
Poisson with mean 8*(0.5) = 4, so now ask: what is the probability
that a Poisson X with mean 4 has a value >= 8? Of course (as in your
second posting) this is 1 - Pr{X <= 7}; however, you used the wrong X
there.

R.G. Vickson,
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