Question

The CEO of an organization read a research article describing the importance of generational influence on work motivation. He is now interested in determining if the distribution of Baby Boomer, Generation X, and Millennial employees is the same across engineering and management positions in his company. Staff in the HR department gather records and provide him with the following information:

Employee Age Group	Number of Managers	Number of Engineers
Baby Boomers	28	18
Generation X'ers	36	34
Millennials	21	45

• Provide the appropriate null and alternative hypotheses.
• Determine which type of analysis would be appropriate to answer this research question. Be specific. Please support your answer using course materials.
• Identify the variables included in this study. Label variables as dependent and independent, if applicable.
• What are the levels of measurement for each variable?
• What are the degrees of freedom associated with the test statistic?

Answer 1

(a)

Null hypothesis is

Alternative hypothesis is

(b)

We have to perform Chi-squared test for independence of variables.

(c)

Here, number of rows and number of columns

So our test statistic will be

where,

is observed cell frequency of i-th row and j-th column.

is observed cell frequency of i-th row and j-th column.

(d)

The variables are

• Age of employees
• Number of employees

To draw conclusion about dependency or independency we have to perform Chi-squared test as follows.

Observed frequency	Number of Employees
Managers	Engineers	Row total
Employee Age Group	Baby Boomer's	28	18	46
Generation X'ers	36	34	70
Millennials	21	45	66
Column total	85	97	182

The contingency table of expected frequencies is as follows.

Expected frequency	Number of Employees
Managers	Engineers	Row total
Employee Age Group	Baby Boomer's	85*46/182 = 21.5	97*46/182 = 24.5	46
Generation X'ers	85*70/182 = 32.7	97*70/182 = 37.3	70
Millennials	85*66/182 = 30.8	97*66/182 = 35.2	66
Column total	85	97	182

Degrees of freedom

[Using R-code '1-pchisq(10.16118,2)']

We reject our null hypothesis if , level of significance.

We generally test for level of significance 0.10, 0.05, 0.01 or something like these.

So, we reject our null hypothesis.

Hence, based on the given data we can conclude that the variables are not independent.

So, the variables are dependent.

(e)

Degrees of freedom associated with the test statistic is 2.