Question

For the following data fit a Poisson distribution and test for goodness of fit at 5% level of significance.

Answer 1

Let x be the no. of mistakes is a poisson variate the parameter is obtained as below: Let f be the no. of pages.

From the above distribution:

Theoretical frequency: T_x = p{x) N
T₀ =p(x = 0)100   x 100 

= 0.3012 x 100 = 30.12

T₅ and more = N – [T₀ + T₁ + T₂ + T₃ + T₄ 

= 100 – [30 + 36 + 22 + 9 + 3] 

= 100 – 100 = 0

The fitted observed and theoretical frequency distribution is:

chi – Square test: H₀ : Poisson distribution is a good fit [O_i = E_i]
Hj: poisson distribution is not good fit [O_i = E_i] {Upper tail test}
Under H₀, the χ² – test stastic is:
λ is estimated from the parameter and so degrees of freedom is (n – 2)

Ay α = 5% for (n – 2) = 4.2 = 2 d.f the upper tail critical value k₂= 5.99

Here χ²_call lies in acceptance region (A.R)
.’. Ho is accepted.
Conclusion: Poisson distribution is good fit.