Suppose we suspected an unusual distribution of blood groups in patients undergo

Question

Suppose we suspected an unusual distribution of blood groups in patients undergoing one type of surgical procedure. We know that the expected distribution for the population served by the hospital which performs this surgery is 44% group O, 45% group A, 8% group B and 3% group AB. We can take a random sample of routine pre-operative blood grouping results and compare these with the expected distribution. Assuming a sample of 313 patients, and the following distribution of blood types in the sample, what is the p-value given by a Chi-squared test for Goodness of Fit? Do not use a Chi-squared table to do the calculations, rather use the online calculator found here: http://graphpad.com/quickcalcs/chisquared1 .cfm (do not click on it as it will open in THIS window and you will lose your work, rather swipe over it with your mouse and copy and paste it into a new browser).

Explanation / Answer

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
112   137.72   4.803357537  
145   140.85   0.12227547  
35   25.04   3.96172524  
21   9.39   14.35485623  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    23.24221448      
          
As df = a - 1,           
          
a =    4      
df = a - 1 =    3      
          
Hence, the p value is          
          
p =    3.59503*10^-5   [ANSWER]  
          

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