The national distribution of fatal work injuries in a country is shown in the table to...

The national distribution of fatal work injuries in a country is shown in the table to the right under
National %. You believe that the distribution of fatal work injuries is different in the western part of the
country and randomly select 5000 fatal work injuries occurring in that region. At
α= 0.10, can you conclude that the distribution of fatal work injuries in the west is different from the
national distribution?

% Actual counts
Category 1 20% 1020
Category 2 30% 1505
Category 3 40% 2100
Category 4 10% 375

Solutions

Expert Solution

H0: Null Hypothesis: The distribution of fatal work injuries in the west is not different from the national distribution

HA:Alternative Hypothesis: The distribution of fatal work injuries in the west is different from the national distribution (Claim)

Test Statistic () is got as follows:

Category	Observed (O)	Expected (E)	(O - E)2/E
Category 1	1020	5000 X 0.20= 1000	0.400
Category 2	1505	5000 X 0.30 = 1500	0.017
Category 3	2100	5000 X 0.40 = 2000	5.000
Category 4	375	5000 X 0.10 = 500	31.250
Total = =			36.667

dt = 4 - 1 = 3

From Table, critical value of =6.251

Since caluclated value of = 36.667 is greater than critical value of = 6.251. the difference is different. Reject null hypothesis.

Conclusion:

The data support the claim that the distribution of fatal work injuries in the west is different from the national distribution (Claim)

orchestra answered 1 year ago

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