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 0.025α=0.025 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.	Cause	National​ %	Western Frequency
	Transportation	4343​%	28942894
	Equipment	1818​%	11571157
	Assaults	1515​%	804804
	Falls	1313​%	746746
	Harmful fumes	88​%	532532
	Fires	33​%	9898

a. State

Upper H 0H0

and

Upper H Subscript aHa

and identify the claim.What is the null​ hypothesis,

Upper H 0H0​?

A.The distribution of fatal work injuries in the west is

28942894

​transportation,

11571157

​equipment,

804804

​assaults,

746746

​falls,

532532

harmful​fumes, and

9898

fires.

B.The distribution of fatal work injuries in the west is

4343​%

​transportation,

1818​%

​equipment,

15 %15%

​assaults,

1313​%

​falls,

88​%

harmful​fumes, and

33​%

fires. Your answer is correct.

C.

The distribution of fatal work injuries in the west differs from the expected distribution.

What is the alternate​ hypothesis,

Upper H Subscript aHa​?

A.The distribution of fatal work injuries in the west is

4343​%

​transportation,

1818​%

​equipment,

15 %15%

​assaults,

1313​%

​falls,

88​%

harmful​fumes, and

33​%

fires.

B.

The distribution of fatal work injuries in the west is the same as the expected distribution.

C.

The distribution of fatal work injuries in the west differs from the expected distribution.

Your answer is correct.

Which hypothesis is the​ claim?

Upper H 0H0

Upper H Subscript aHa

Your answer is correct.b. Determine the critical​ value,

font size increased by 1 font size increased by 1 font size increased by 1 chi Subscript 0 Superscript 2χ20​,

and the rejection region.

Answer 1

critical value X²₀ =12.833

rejection region X² >=X²₀

Applying chi square test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1.000	0.430	2894	2679.33	4.15	17.200
2.000	0.180	1157	1121.58	1.06	1.119
3.000	0.150	804	934.65	-4.27	18.263
4.000	0.130	746	810.03	-2.25	5.061
5.000	0.080	532	498.48	1.50	2.254
6.000	0.030	98	186.93	-6.50	42.308
total	1.000	6231	6231		86.204

test statistic X² =86.204

(p value =0.0000 ; reject Ho)