Question

The safety director of a large steel mill took samples at random from company records of...

The safety director of a large steel mill took samples at random from company records of minor work-related accidents and classified them according to the time the accident took place.

Number of Number of
Time Accidents Time Accidents
8 up to 9 a.m. 8 1 up to 2 p.m. 8
9 up to 10 a.m. 4 2 up to 3 p.m. 10
10 up to 11 a.m. 8 3 up to 4 p.m. 9
11 up to 12 p.m. 11 4 up to 5 p.m. 12

Click here for the Excel Data File

Using the goodness-of-fit test and the 0.02 level of significance, determine whether the accidents are evenly distributed throughout the day.

H0: The accidents are evenly distributed throughout the day.   
H1: The accidents are not evenly distributed throughout the day.

State the decision rule, using the 0.02 significance level. (Round your answer to 3 decimal places.)

Compute the value of chi-square. (Round your answer to 3 decimal places.)

What is your decision regarding H0?

Math   Statistics-And-Probability   
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Homework Answers

Answer #1
degree of freedom =categories-1= 7
for 0.02 level and 7 df :crtiical value X2 = 16.622      from excel: chiinv(0.02,7)
Decision rule: reject Ho if value of test statistic X2>16.622
applying chi square goodness of fit test:
           relative observed Expected Chi square
Category frequency(p) Oi Ei=total*p R2i=(Oi-Ei)2/Ei
1 1/8 8 8.75 0.064
2 1/8 4 8.75 2.579
3 1/8 8 8.75 0.064
4 1/8 11 8.75 0.579
5 1/8 8 8.75 0.064
6 1/8 10 8.75 0.179
7 1/8 9 8.75 0.007
8 1/8 12 8.75 1.207
total 1.00 70 70 4.74
test statistic X2= 4.743

decision regarding H0 :

Fail to reject Ho ; since test statistic < critical value

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