Question on calculating p-value

Suppose X is a Poisson random variable with parameter a

In a hypothesis test we wish to test:

H0 (Null): a<=10

H1: a>10

The rejection region is x>=16

Suppose we observe x=18

what is the p-value of the test?

I'm not sure really what this is asking, any hints anyone?

Re: Question on calculating p-value

Hey darren86.

The p-value corresponds to the probability value that H0 is not rejected on the basis of the data.

Basically you need to find the probability P(X >= 16) where X is the distribution you are using for your hypothesis.

If you have one observation then use the MLE estimator and find out when the parameter is greater than 10 and what that implies for your sample.

Then given a > 10, find out what the x value of 16 is in terms of the probability P(X >= 16) and this will be your significance value that is used to reject or fail to reject the null hypothesis.

The typical value used in many tests is the classic 0.05 rejection (or 95% confidence interval).

Re: Question on calculating p-value

Hi darren86!

If you have a Poisson distribution with parameter 10 (the null hypothesis), what is the chance to find 16 or more occurrences in a time interval?

And what is the chance to find 18 or more occurrences in a time interval?