Question

The number of accidents in a highway as recorded every month over a 9 - month periods are 15,18,9,11,14,10,8,13,19. Test at 5% frequencies are in agreement with the belief that the number of accidents was the same during the 9 - months. it is given that the table values of x² at 5% level for 8 d.o.f and 9 d.o.f . are 15.5 and 16.9 respectively.

Answer 1

Let,

$H_o:$ The number of accidents ocur during 9 months are same with expected frequencies $(E_i=\dfrac{N}{9}=\dfrac{117}{9}=13)$

The distribution table is-

ob_freq_Oi  Exp_freq_Ei    square of(Oi-Ei)
15          13             4
18          13             25             
9           13             16
11          13             4
14          13             1
10          13             9
 8          13             25
13          13              0
19           13             36

The value of $\chi^2=\sum{\dfrac{(O_i-E_i)^2}{E_i}}=\dfrac{120}{13}=9.2307$

The tabulated value of $\chi^2$ at 8 d.o.f. is 15.5

Conclusion: As the calculated value of $\chi^2$ is less than the standard value so, Null hypothesis is accepted i.e. Number of accidents are same.