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

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written 6.9 years ago by

teamques10 ★ 70k

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

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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