Question

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.		10			1 up to 2 p.m.		9
9 up to 10 a.m.		19			2 up to 3 p.m.		20
10 up to 11 a.m.		9			3 up to 4 p.m.		6
11 up to 12 p.m.		8			4 up to 5 p.m.		7

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Using the goodness-of-fit test and the 0.01 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 0.01 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?

Answer 1

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

observed frequencey, O	expected proportion	expected frequency,E			(O-E)²/E
10	0.125	11.00			0.091
19	0.125	11.00			5.818
9	0.125	11.00			0.364
8	0.125	11.00			0.818
9	0.125	11.00			0.364
20	0.125	11.00			7.364
6	0.125	11			2.273
7	0.125	11			1.455

chi square test statistic,X² = Σ(O-E)²/E =   18.545              
                  
level of significance, α=   0.01              
Degree of freedom=k-1=   8   -   1   =   7
                  
P value =   0.0097   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value < α, Reject Ho                  

............

THANKS

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