Question

A survey across generations of workers gathered data on engagement at work. The results for a sample of​ 1,000 workers are in the accompanying contingency table. At the 0.10 level of​ significance, is there evidence of a significant relationship between generation and level of engagement in the​ workplace?

Millennials Gen Xers Baby Boomers Traditionalists Engaged 100 116 90 18 Not Engaged 190 149 134 17 Actively Disengaged 56 65 59 6 What are the null and Alt. Hypothesis?

Answer 1

Data Summary

Observed Frequencies (O)	Millennials	Gen Xers	Baby Boomers	Traditionalists	Total
Engaged	100	116	90	18	324
Not Engaged	190	149	134	17	490
Actively Disengaged	56	65	59	6	186
Total	346	330	283	41	1000

The null and alternative hypotheses are                  
Ho :      There is a no significant relationship between Generation and Level of engagement at workplace .

Ha :      There is a a significant relationship between Generation and Level of engagement at workplace .                               
α = 0.10                  
We use Chi Square test of independence                  
                  
Grand Total of frequencies n = 1000                  
To find Expected Frequencies                  
Expected Frequencies = (Row Total * Column Total)/Grand Total                  

Expected Frequencies (E)	Millennials	Gen Xers	Baby Boomers	Traditionalists
Engaged	112.104	106.92	91.692	13.284
Not Engaged	169.54	161.7	138.67	20.09
Actively Disengaged	64.356	61.38	52.638	7.626

Following table gives the value of (Observed - Expected)² / Expected

	Millennials	Gen Xers	Baby Boomers	Traditionalists
Engaged	1.3069	0.7711	0.0312	1.6742
Not Engaged	2.4691	0.9975	0.1573	0.4753
Actively Disengaged	1.0849	0.2135	0.7689	0.3467

Chi Square Value = ∑[(Observed - Expected)² / Expected]                  
χ² = 10.2966                  
                  
Degrees of freedom = df = (number of rows - 1) * (number of columns - 1)                  
Degrees of freedom = df = 6                  
                  
From chi square table or CHISQ.DIST.RT(X, df) function of Excel                  
we find the p-value                  
p-value = CHISQ.DIST.RT( 10.2966, 6) = 0.1127                  
p-value = 0.1127           
                  
Decision :                  
0.1127 > 0.1                  
that is p-value > α                  
Hence we DO NOT REJECT Ho                  
                   
Conclusion :                  
There does not exist enough statistical evidence at α = 0.1 to show that                   
there is a significant relationship between Generation and Level of engagement at workplace.

that is there is no significant relationship between Generation and Level of engagement are independent