Question

Goodness of Fit Test 5. Aresearcher wanted to determine bicycle deaths were uniformly distributed over the days of the week. She randomly selected 200 deaths by bicycles, recorded the days they happened with the following data Monday Fuesday Wednesday Thursday Friday Saturday 16 35 16 28 34 30 s there evidence to believe that bicycle deaths occur with equal frequency with respect to day of the week at a 0.05 level of significance

Answer 1

5 )

The hypothesis are :

H0 : Bicycle deaths occur with equal frequency with respect to day.

H1: Bicycle deaths occur with unequal probability with respect to day.

The test statistic is

O = Observed frequency

E = Expected frequency

E = N* p

All days have same probability. So p = 1/7 and N= 200.

Hence expected frequency = E = 200 * 1/7 = 28.57 for each day.

O	E
16	28.57	5.530
35	28.57	1.447
16	28.57	5.530
28	28.57	0.011
34	28.57	1.032
41	28.57	5.408
30	28.57	0.072
	Total	19.031

So, test statistic is

= 19.031

df = Number of days - 1 = 7 -1 = 6 , = 0.05

In the chi square probability table , we look across df = 6 and probability 0.05 .

So the critical value =

Here calculated value of > critical value of

Hence we reject null hypothesis.

Conclusion : There is no evidence to believe that bicycle deaths occur with unequal frequency with respect to day.