Question

Fit a Poisson distribution to the following data and test the goodness of fit at 5% level of significance

Answer 1

Let X be the number of mistakes is a poisson variate with λ is obtained as below:- let f be the no of pages, then from the frequency disribution:

The fitted theoretical and observed frequency distribution is:- (Approximated)

χ² -TEST: H₀: poisson distribution is good fit (0_i = E_i)

H₁: poisson distribution is not a good tit (0_i ≠ E_i)

Under H₀, the χ²-test statistic is:-

Here λ is estimated from the data and so d.f. will be (n – 1 – 1) = (n – 2)

∴ χ_cal² = 1-8309

At α = 5% for (n – 2) = 6 – 2 = 4d.f the upper tail critical value k² = 9.49.

Here χ_cal² lies in acceptance region.

∴ H₀ is accepted Conclusion: Poisson distribution is good fit (0_i = E_i).