Question

A survey of 100,000 college graduates and 100,000 non-college graduates is conducted to determine how many of them own stock. 49,781 of the non-college graduates own stock vs. 50,219 for the college graduates. Analyze for a relationship between education and owning stock using a chi-square hypothesis test with alpha=1%.

Answer 1

Data Summary

Observed Frequencies (O)	College	Non-college
Own stock	50219	49781
Do not own stock	49781	50219

The null and alternative hypotheses are   
Ho : Education and Owning stock are independent   
Ha : Education and Owning stock are dependent   
   
Level of significance α = 0.01   
We use Chi Square test of independence   
   
Grand Total of frequencies = 200000   
To find Expected Frequencies   
Expected Frequencies = (Row Total * Column Total)/Grand Total   

Expected Frequencies (E)	College	Non-college
Own stock	50000	50000
Do not own stock	50000	50000

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

	College	Non-college
Own stock	0.9592	0.9592
Do not own stock	0.9592	0.9592

Chi Square Value = ∑[(Observed - Expected)² / Expected]   
χ² = 3.8369   
   
Degrees of freedom = df = (number of rows - 1) * (number of columns - 1)   
Degrees of freedom = df = 1   
   
From chi square table or CHISQ.DIST.RT(X, df) function of Excel   
we find the p-value   
p-value = CHISQ.DIST.RT( 3.8369, 1) = 0.0501   
p-value = 0.0501   

Decision :   
0.0501 > 0.01   
that is p-value > α   
Hence we DO NOT REJECT Ho   
      
Conclusion :   
There does not exist enough statistical evidence at α = 0.01 to show that Education and Owning stock are dependent.

that is

There is no relationship between Education and Owning stock.