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.