Skittles candies have multiple colors in each bag Unlike oth

Skittles candies have multiple colors in each bag. Unlike other candies, each color is said to be found in equal amounts in each bag. A student got a large bag of Skittles and found the following distribution of Skittles:

Red

Orange

Yellow

Green

Purple

16

24

23

10

27

Write the null and alternate hypothesis for this test.

Calculate the expected counts and then complete the chi-square goodness of fit test for this data.

Write a conclusion to this data.

Solution

Ho: There are equal amounts of candies of each color in each bag.

Ha: There are not equal amounts of candies of each color in each bag.

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If Ho is true, then there should be 20 candies on the average for each color.

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
16   20   0.8  
24   20   0.8  
23   20   0.45  
10   20   5  
27   20   2.45  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    9.5      
          
As df = a - 1,           
          
a =    5      
df = a - 1 =    4      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      
chi^2(crit) =    9.487729037      
          
Also, the p value is          
          
p =    0.049747247      
          
Thus, comparing chi^2 > chi^2(crit) [or, p<0.05], we   REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that there are not equal amounts of candies of each color in each bag. [CONCLUSION]