Question

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 6231 fatal work injuries occurring in that region. At alpha equals 0.10α=0.10 can you conclude that the distribution of fatal work injuries in the west is different from the national​ distribution? Complete parts a through d below. calculate test statistic and determine whether to reject/ fail to reject null hypothesis, if there is/ is not enough evidence to conclude western fatal injuries are the same as/ differ from the national distribution.	Cause	National​ %	Western Frequency
	Transportation	43​%	288
	Equipment	19​%	1156
	Assaults	15​%	806
	Falls	13​%	750
	Harmful fumes	88​%	531
	Fires	22​%	100

Answer 1

1. State the hypotheses.

H0: The distribution of fatal work injuries in the west is same as the national​ distribution
H1: The distribution of fatal work injuries in the west is different from the national​ distribution

2. Formulate an analysis plan.

For this analysis, the significance level is 0.10. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.

3. Analyze sample data.

Expected count for seeds under each category if null hypothesis is true, Ei = n * pi

E1 = 6231 * 0.43 = 2679.33
E2 = 6231 * 0.19 = 1183.89
E3 = 6231 * 0.15 = 934.65
E4 = 6231 * 0.13 = 810.03

E5 = 6231 * 0.08 = 498.48

E6 = 6231 * 0.02 = 124.62

Chi-square test statistic =

= 46.0508

4. Decision

Degree of freedom = k-1 = 6-1 = 5

Critical value of Chi Square value at df = 5 and 0.10 significance level is 9.236.

Since the observed test statistic (46.0508) is greater than the critical value (9.236) , we reject H0.

5. Conclusion

There is significant evidence from the sample data that the distribution of fatal work injuries in the west is different from the national​ distribution.