# Thread: normal approximation of the poisson

1. ## normal approximation of the poisson

have data, want to conduct hypothesis test using a normal approximation to the poission distribution,

H0: mean=1
H1: mean>1

thanks for the help

2. I assume you have a sample and just want to standardize it....

Use ${\bar X-\mu\over \sigma/\sqrt{n}}$ as your test statistic

Here $\lambda=\mu=\sigma^2$

Under the null $\lambda=\mu=\sigma^2=1$

3. how would i calculate lamba from the data though,

thanks

4. the sample estimate of lambda WOULD be the sample mean, for say confidence intervals.

BUT here you are assumming, under the null, that lambda which is the mean is ONE

SO use ${\bar X-1\over 1/\sqrt{n}}$ as your test statistic

5. aha ok i understand thanks a lot

6. BUT n must be large