i) Apply the Chi-Square test to these data to test the hypothesis that the underlying distribution is Poisson.

ii) Apply the Chi-Square test to these data to test the hypothesis that the underlying distribution is Poisson with mean 1.0. Use level of significance $\alpha$= 0.05 and $\chi ^2$= 5.99, $\chi ^2 _{0.05,3}$= 7.81

i) Define hypothesis

$H_0:$ data fits to Poisson distribution

$H_a:$ data does not fits to Poisson distribution

For Poisson distribution,

$P_{i}=\frac{e^{-\alpha} \alpha^x}{x !}$

$\alpha=\overline{x}=\frac{\sum f_{i} m_{i}}{n}$

$\therefore \alpha = \frac{0 \times 35 + 1 \times 40 + 2 \times 13 + 3 \times 6 + 4 \times 4 + 5 …