It is sometimes said that older people are overrepresented o

It is sometimes said that older people are overrepresented on juries. Display 12.15 gives information about people on grand juries in Alameda County, California. Assuming the 66 people can be considered a random sample of people on grand juries in this county, is there statistically significant evidence that the distribution of ages of grand jurors is not the same as the distribution of ages in the county?

Solution

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
5   27.72   18.6218759  
9   15.18   2.515968379  
19   10.56   6.745606061  
33   12.54   33.38210526  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    61.26555561      
          
As df = a - 1,           
          
a =    4      
df = a - 1 =    3      
          
Thus, the p value is          
          
p =    3.15373E-13      
          
As this is a very small P value, then we reject the suggested distribution.
          
Thus, there is significant evidence that the distribution of ages of grand jurors is not the same as the distribution of ages in the county. [CONCLUSION]