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The following table gives the number of accidents in a city during a week. Find whether the accidents are uniformly distributed over a week.
Day Sun Mon Tue Wed Thu Fri Sat Total
No. of Accident 13 15 9 11 12 10 14 84

1 Answer
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i. Null hypothesis $\ (H_0)$: Accidents are equally distributed over all the days of week.

Alternative Hypothesis $\ (H_a)$ : Accidents do hot occur equally.

ii. Calculation of test statics: If the accidents occur equally on all days of a week, than there will be $ \frac {84}{7} = 12$ accident per day, i.e E=12

Day Observed frequency (O) Expected Frequency (E) $\ (O-E)^2$ $\ X^2 = \frac {(O-E)^2}{E}$
Sun 13 12 1 0.0833
Mon 15 12 9 0.75
Tue 11 12 1 0.0833
Wed 9 12 9 0.75
Thu 12 12 0 0
Fri 10 12 4 0.3333
Sat 14 12 4 0.3333
Total $\sum{x^2}$ = 2.33

iii. Level of significance: $ \alpha$ = 0.05

Degree of freedom = h-1

=7-1

=6

iv Critical value $ \Rightarrow$ For 6 degrees of freedom at 5% level of significance table value.

$\ x^2$ is 12.59

v. Decision $ \Rightarrow$ Since the calculated value of $\ x^2$ is less than the table value. The hypothesis is accepted.

$\therefore$ The accidents occur equally on all working days.

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