Question

1. A recent study of accident records at a large engineering company reported the following number of injuries in each shift for one year: Morning, 879; Afternoon, 1,067; Night, 1,200. Is there sufficient evidence to say that the number of accidents during the three shifts are not the same? Test at the α = 0.05, α = 0.01, and α = 0.001 levels.

a. There is sufficient evidence at the 0.05 level but not at the 0.01 and 0.001 levels.

b. There is sufficient evidence at both 0.05 and 0.01 levels but not at the 0.001 level.

c. There is sufficient evidence at the 0.001 level but not at the 0.05 and 0.01 levels.

d. There is sufficient evidence at all three levels to say that the number of accidents during each shift are not the same.

Answer 1

Total of injuries in one year = 879 + 1067 + 1200 = 3146

Expected number of injuries in each shift = (1/3) * 3146 = 1048.667

Chi Square test statistic,

= 49.61028

Degree of freedom = 3 - 1 = 2

P-value = P( > 49.61028 , df = 2) = 0.0000

Since p-value is less than 0.001, 0.01 and 0.05,

d. There is sufficient evidence at all three levels to say that the number of accidents during each shift are not the same.