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	82	106	78
Information	47	56	58
Financial	83	106	115

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

• do not reject H0H0
• 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 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.
• There is not enough evidence to support the claim that the length of unemployment is dependent of the type of industry.

Answer 1

1)

Expected	Ei=row total*column total/grand total	pop 1	pop 2	pop 4
	row 1	77.144	97.521	91.335
	row 2	46.692	59.026	55.282
	row 3	88.164	111.453	104.383

2)

Applying chi square test of independence:

chi square    χ2	=(Oi-Ei)2/Ei	pop 1	pop 2	pop 4	Total
	row 1	0.306	0.737	1.947	2.9899
	row 2	0.002	0.1551	0.1337	0.2908
	row 3	0.302	0.2668	1.0799	1.6491
	total	0.6102	1.1591	3.1605	4.930
test statistic X2 =		4.930
p value =		0.295

do not reject H0

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