Question

Is the length of time of unemployment related to the type of industry? A random sample of unemployed workers from three different work sectors yielded the following data. Perform a hypothesis test at 0.10 level of significance to determine if there is a relationship.

	Less than 5 weeks	5-14 weeks	15-26 weeks
Transportation	80	107	84
Information	56	55	51
Financial	86	111	112

What are the expected numbers? (round to 3 decimal places)

	Less than 5 weeks	5-14 weeks	15-26 weeks
Transportation
Information
Financial

The hypotheses are

H0:H0: The length of unemployment is independent of the type of industry.

HA:HA: The length of unemployment is dependent of the type of industry. (claim)

Since αα = 0.10 the critical value is 7.779

The test value is: (round to 3 decimal places)

The p-value is (round to 3 decimal places)

So the decision is to

• reject H0H0
• do not reject H0H0

Thus the final conclusion is

• There is enough evidence to support the claim that the length of unemployment is dependent of the type of industry.
• There is not enough evidence to support the claim that the length of unemployment is dependent of the type of industry.
• There is enough evidence to reject the claim that the length of unemployment is dependent of the type of industry.
• There is not enough evidence to reject the claim that the length of unemployment is dependent of the type of industry.

Answer 1

The Expected value data are in the table below. Each Cell = Row total * Column Total/N. N = 742

The degrees of freedom, df = (r – 1) * (c -1) = (3 - 1) * (3 - 1) = 4

Expected
	<5	5-14'	15-26	Total
Transportation	81.081	99.708	90.212	271
Information	48.469	59.604	53.927	162
Financial	92.450	113.689	102.861	309
Total	222	273	247	742

_____________________________________________________

The Test Statistic: The table below gives the calculation of .

#	Observed	Expected	(O-E)	(O-E)2	(O-E)2/E
1	80	81.081	-1.0809	1.168345	0.0144
2	56	48.469	7.531	56.71596	1.1701
3	86	92.450	-6.4501	41.60379	0.4500
4	107	99.708	7.2925	53.18056	0.5334
5	55	59.604	-4.6038	21.19497	0.3556
6	111	113.689	-2.6887	7.229108	0.0636
7	84	90.212	-6.2116	38.58397	0.4277
8	51	53.927	-2.9272	8.5685	0.1589
9	112	102.861	9.1388	83.51767	0.8119
Total					3.986

test = 3.986

The p value: The p value at test = 3.986, df = 4; P value = 0.408

The Decision: Since p value is > (0.10), Do Not Reject H0.

The Conclusion: Option 2: There is not enough evidence to support the claim that the length of unemployment is dependent of the type of industry.