Question

According to traffic engineers. roundabouts, or traffic circles, result in traffic accidents occurring more or less evenly across all intersections where they are installed (rather than certain intersections being particularly bad for accidents). To test this Region of Waterloo staff select a random sample of reports involving 150 accidents occurring along Ira Needles Boulevard in Waterloo which contains six roundabouts. The following is the distribution of accidents by location for this sample. Intersection Frequency Erb 33 University 28 Boardwalk 19 Victoria 30 Highland 22 Highview 18 N=150 Test the hypothesis that roundabouts even out the incidence of accidents. Use the .o5 significance level.

Answer 1

a) As we are testing here whether the traffic accidents occurring more or less are evenly across all intersections, therefore this is a test for independence here. The null and the alternative hypothesis here are obtained as: H0: Independence and H1: Dependence.

Therefore C is the correct answer here.

b) The expected frequency for each of the 6 categories here is computed as:
E = 150/6 = 25

The chi square test statistic here is computed as:

1* = [ (0; – E:)! E;

2 82 + 32 +6° +5+3+72 25 = 7.68

Therefore 7.7 is the required chi square test statistic value here.

c) For k - 1 = 5 degrees of freedom, we have from chi square distribution tables here: (for 0.05 level of significance )

P(AB < 11.0705) = 0.95 לת

Therefore,
$P(\chi^2_5 > 11.0705) = 1 - 0.95 = 0.05$

Therefore 11.0705 is the required critical value here.

d) As the test statistic value here is 7.7 < 11.0705, therefore it lies in the non rejection region here and we cannot reject the null hypothesis here. Therefore we accept the null hypothesis here and conclude that the distribution is equal here.