hypothesis testing using poisson distribution

Question

At a nuclear plant great care is taken to measure the employees health.These are the number of visits made by each of the 10 employees to the doctor during a calender year. 3,6,5,7,4,2,3,5,1,4

Assuming the number of visits made by employee has a poisson distribution ,test the hypothesis that the annual mean per employee is greater than 3.

I am using the graphical method and I am not sure of which p[X=x] should i consider.

X: no.of visits by each employee to the doctor.

H0:lambda=3
H1:lambda>3
X follows a Poisson(3)

Then what is the probability that I should check?

What I did was as the average of sample data is 4.73636. Therfore calculated p[X>=4] and checked if it was in the critical region. Is this the correct probability to calculate? In a poisson distribution the expected value is calculated as x*p[X=x] right?Not as (sigma x*f(x))/(sigma x)

Please add the homework or self-study tag as is appropriate; it helps us decide whether to just give you the answer or guide you to it. — jbowman, Oct 28 '13 at 01:27
Obviously, that's why you posted, but that's not what I asked. Where did the question come from? — Glen_b, Oct 31 '13 at 14:55

score 0 · Accepted Answer · answered Oct 28 '13 at 14:12

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Clarkson - a convenient method for this particular problem will be to recognise that the sum of poisson variables is also poisson. In this case, you would model the total number of visits in the year as poisson(30) and see what you can infer from there.

answered Oct 28 '13 at 14:12

Thanks.Then I should look for P[X>=40] right? As there is a total of 40 days.One question.Should my null hypothesis change into H0:lambda=30 or is it lamda=3 – clarkson Oct 28 '13 at 15:52
Yes, lambda = 30, so you average 3 vistits per year per employee. This will be a one sided test, you want to calculate the probability $P(X\geq 40)$ under the null. – Oct 28 '13 at 16:03

hypothesis testing using poisson distribution

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