Question

The safety director of an insurance company took samples at random from his minor accidents file and classified them according to the time the accident took place.

Time Number of Accidents
8 - 9 am 6
9 - 10 am 6
10 - 11 am 20
11 - 12 noon 8
1 - 2 pm 7
2 - 3 pm 8
3 - 4 pm 19
4 - 5 pm 6
Using the chi-square test and the .01 level of significance, determine whether or not the accidents are evenly distributed throughout the day.
a) What are the Null and Alternate Hypotheses?
b) What is the critical value?
c) What is the Decision Rule?
d) What is the test statistic?
e) What is the decision?
f) What does the decision infer?

Answer 1

Explanation:

A. H0: accident are evenly distributed

H1: accident are not evenly distributed

B. The critical value is chi²(0.01,7) = 18.4753

C. The decision rule would be to reject h0 and accept h1 if the test statistic is higher than the critical value

D. Test statistic = summation (Oi-Ei)²/E

This gives 24.6 from the table.

E. Based on these calculations, test statistic is > than critical value

24.6> 18.4753

F. The inference is that accidents are not evenly distributed at 0.01 level of significance.