Question

Fit a poisson distribution to the following data and test for goodness of fit.

Answer 1

H₀ : Poisson distribution is a good fit to the observed data/distribution

H₁ : Poisson distribution is not a good fit to the observed data/distribution.

To test H₀ , we fit a poisson distribution to the data

So, the parameter can be estimated by finding mean

Let 0 and E be the observed (f) and expected (T_x) frequencies, the

Here n = 4 . χ²_cal = 26.66

At α = 5% the upper Tail critical value for (n – 2) (4 – 2) 

= 2 d.f is k = 5.99.

Here χ²_cal > k.

∴ H₀ is rejected and H₁ is accepted.

Conclusion : Poisson distribution is not a good fit.