The amounts of vitamin c (in milligrams) for 100 g (3.57 ounces) of various rand

Question

The amounts of vitamin c (in milligrams) for 100 g (3.57 ounces) of various randomly selected fruits and vegetables are listed. Is there sufficient evidence to conclude that the standard deviation differs from 12 mg?


7.9, 16.3, 12.8, 13.0, 32.2, 28.1, 46.4, 53.0, 15.4, 18.2, 25.0, 5.2, 34.4

I would like to know how to calculate the S i know the s will be 14.60 but i wanna know how do you get that 14.60! ive been trying to calculate but its totally a different number evo though i made sure that im doing it correctly !

Explanation / Answer

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    307.9      
As n =    13      
Thus,          
X =    23.68461538      
          

Setting up tables,

          
Thus, Sum(x - X)^2 =    2560.656923      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    13      
          
s^2 =    213.3880769      
          
Thus,          
          
s =    14.60780877 [ANSWER]

x x - X (x - X)^2 7.9 -15.7846 249.1541 16.3 -7.38462 54.53254 12.8 -10.8846 118.4749 13 -10.6846 114.161 32.2 8.515385 72.51178 28.1 4.415385 19.49562 46.4 22.71538 515.9887 53 29.31538 859.3918 15.4 -8.28462 68.63485 18.2 -5.48462 30.08101 25 1.315385 1.730237 5.2 -18.4846 341.681 34.4 10.71538 114.8195

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