Question

In: Math

Suppose a company surveyed the work preferences and attitudes of 1,006 working adults spread over three...

Suppose a company surveyed the work preferences and attitudes of 1,006 working adults spread over three generations: baby boomers, Generation X, and millennials. In one question, individuals were asked if they would leave their current job to make more money at another job. The sample data are summarized in the following table.

Leave Job for More Money?	Generation
Leave Job for More Money?	Baby Boomer	Generation X	Millennial
Yes	119	153	173
No	197	184	180

Conduct a test of independence to determine whether interest in leaving a current job for more money is independent of employee generation.

State the null and alternative hypotheses.

H₀: Interest in leaving job for more money is not mutually exclusive of the employee generation.
H_a: Interest in leaving job for more money is mutually exclusive of the employee generation.

H₀: Interest in leaving job for more money is independent of the employee generation.
H_a: Interest in leaving job for more money is not independent of the employee generation.

H₀: Interest in leaving job for more money is not independent of the employee generation.
H_a: Interest in leaving job for more money is independent of the employee generation.

H₀: Interest in leaving job for more money is mutually exclusive of the employee generation.
H_a: Interest in leaving job for more money is not mutually exclusive of the employee generation.

Find the value of the test statistic. (Round your answer to two decimal places.)

What is the p-value? (Round your answer to four decimal places.)

Using a 0.05 level of significance, what is your conclusion?

Do not reject H₀. We conclude that interest in leaving a job for more money is not independent of the employee generation.

Reject H₀. We conclude that interest in leaving a job for more money is not independent of the employee generation.

Do not reject H₀. We cannot conclude that interest in leaving a job for more money is independent of the employee generation.

Reject H₀. We cannot conclude that interest in leaving a job for more money is independent of the employee generation.

Expert Solution

H₀: Interest in leaving job for more money is independent of the employee generation.
H_a: Interest in leaving job for more money is not independent of the employee generation.

Test Statistic

O : Observed Frequency

E: Expected Frequency

Given,

	Generation
Leave Job for More Money?	Baby Boomer	Generation X	Millennial	Row Total
Yes	119	153	173	445
No	197	184	180	561
Column Total	316	337	353	1006

Expected Frequency:E

Leave Job for More Money?	Baby Boomer	Generation X	Millennial	Row Total
Yes	(445*316) / 1006	(445*337) / 1006	(445*353) / 1006	445
No	(561*316) / 1006	(561*337) / 1006	(561*353) / 1006	561
Column Total	316	337	353	1006

Expected Frequency:E

	Generation
Leave Job for More Money?	Baby Boomer	Generation X	Millennial	Row Total
Yes	139.7813	149.0706	156.1481	445
No	176.2187	187.9294	196.8519	561
Column Total	316	337	353	1006

O	E	O-E	(O-E)²	(O-E)²/E
119	139.7813	-20.7813	431.8629	3.0896
153	149.0706	3.9294	15.4404	0.1036
173	156.1481	16.8519	283.9862	1.8187
197	176.2187	20.7813	431.8629	2.4507
184	187.9294	-3.9294	15.4404	0.0822
180	196.8519	-16.8519	283.9862	1.4426
			Total	8.9874

Value of the test statistic = 8.99

Degrees of freedom = (Number of rows -1)x(Number of columns - 1) = (2-1)x(3-1)=2

For 3 degrees of freedom,

p-value = 0.0112

level of significance: =0.05

As p-value : 0.0112 < level of significance: :0.05; Do not reject H_o

Do not Reject H_o : We can not conclude that interest in leaving a job is not independent of the employee generation

milcah answered 1 year ago

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