# hypothesis testing using poisson distribution

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. Commented Oct 28, 2013 at 1:27
• How does this question arise? Commented Oct 28, 2013 at 3:44
• I want an explanation of how I can solve this please Commented Oct 28, 2013 at 7:37
• Obviously, that's why you posted, but that's not what I asked. Where did the question come from? Commented Oct 31, 2013 at 14:55

• 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.