In a biology laboratory the mating of two red eye fruit flie

In a biology laboratory the mating of two red eye fruit flies yielded n = 432 offspring among which
254 were red-eyed, 69 were brown-eyed, 87 were scarlet-eyed, and 22 were white-eyed. Use these
data to test, with = 0.05, the hypothesis that the ratio among the offspring would be 9:3:3:1
respectively.

Solution

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
254   243   0.497942387  
69   81   1.777777778  
87   81   0.444444444  
22   27   0.925925926  

          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    3.646090535      
          
As df = a - 1,           
          
a =    4      
df = a - 1 =    3      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      

chi^2(crit) =    7.814727903      
          
Also, the p value is          
          
p =    0.302303068      
          
Thus, comparing chi^2 < chi^2(crit) [or, with p > 0.05], we   FAIL TO REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that the distribution here is 9:3:3:1. [CONCLUSION]