Use $x^2$ test to check whether these frequencies are in agreement with the belief that occurrence of accidents was the same during 10 months period. Test at $5\%$ level of significance.

Mumbai University > COMPS > Sem 4 > Applied Mathematics 4

Marks : 08

Year : DEC 2014

Step 1:

Null Hypothesis $(H_0):$ Accidents are uniformly distributed during 10 months period

Alternative Hypothesis $(H_a) =$ Accidents are not uniformly distributed during 10 months period.

Step 2: Test statistic

Total accidents $= 120$

If equally distributed, expected accidents per day $= 120/10 = 12$

Since frequency for 4th and 5th months is less than 10 we combine them.

Similarly, frequency for 7th and 8th month is less than 10, so we combine them.

Step 3: LOS = 5%

Degree of freedom $= n – 1 – 2 = 10 – 3 = 7$

Critical value $(x_x^2) = 14.0671$

$x_{cal}^2=\sum \dfrac {(O-E)^2}E=19.9167$

Step 4: Decision

Since $x_{cal}^2 \gt x_x^2, H_0$ is rejected

Accidents are not uniformly distributed during 10 months period.