A coworker claims that Skittles candy contains equal quantities
of each color (purple, green, orange, yellow, and red). In other
words, 1/5 of all Skittles are purple, 1/5 of all Skittles are
green, etc. You, an avid consumer of Skittles, disagree with her
claim. Test your coworker's claim at the α=0.01α=0.01 level of
significance, using the data shown below from a random sample of
200 Skittles.
Which would be correct hypotheses for this test?
Sample Skittles data:
Color | Count |
---|---|
Purple | 49 |
Green | 49 |
Orange | 43 |
Yellow | 31 |
Red | 28 |
Test Statistic:
Give the P-value. Express to two decimal places:
Which is the correct result:
Which would be the appropriate conclusion?
Solution:
Given:
Claim: Skittles candy contains equal quantities of each color (purple, green, orange, yellow, and red).
Part a) Which would be correct hypotheses for this test?
H0: Skittles candy colors come in equal quantities;
H1: Skittles candy colors do not come in equal quantities
Part b) Test Statistic:
Chi square test statistic for goodness of fit
Where
Oi = Observed Counts
Ei =Expected Counts = N / k = 200 /5 = 40
Thus we need to make following table
Color | Oi: Observed Count | Ei: Expected counts | Oi2/Ei |
Purple | 49 | 40 | 60.025 |
Green | 49 | 40 | 60.025 |
Orange | 43 | 40 | 46.225 |
Yellow | 31 | 40 | 24.025 |
Red | 28 | 40 | 19.600 |
N = 200 |
Thus
Part c) Give the P-value. Express to two decimal places:
To get exact P-value , use Excel command:
=CHISQ.DIST.RT( x , df )
where
x = and df = k - 1 = 5 -1 = 4
=CHISQ.DIST.RT(9.900,4)
=0.0421
=0.04
P-value = 0.04
To get P-value for Chi-square table, look in table for df = 4 row and find interval in which 9.990 fall and then find corresponding right tail area.
fall between 9.488 and 11.143
thus 0.025 < P-value < 0.050
Part d) the correct result:
Since P-value = 0.04 > 0.01 level of significance, we Do not Reject the Null Hypothesis.
Part e) the appropriate conclusion:
There is not enough evidence to reject the claim that Skittles colors come in equal quantities.
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