Skittles candies have multiple colors in each bag. Unlike other candies, each co
ID: 3382928 • Letter: S
Question
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.
Red
Orange
Yellow
Green
Purple
16
24
23
10
27
Explanation / Answer
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.
********************************
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]
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