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 a = 0.10 level of significance, using the data shown below from a random sample of 200 Skittles.
Which would be correct hypotheses for this test?
Ho: Skittles candy colors come in equal quantities; H₁: Skittles candy colors do not come in equal quantities
Ho: Red Skittles are cherry flavored; H₁: Red Skittles are
strawberry flavored
Ho:PP: H₁:P1 P2
Ho: Taste the Rainbow; H₁: Do not Taste the Rainbow
The Correct Answer and Explanation is :
The correct hypotheses for this test would be:
Ho: Skittles candy colors come in equal quantities (i.e., 1/5 of all Skittles are purple, 1/5 are green, 1/5 are orange, 1/5 are yellow, and 1/5 are red).
H₁: Skittles candy colors do not come in equal quantities.
Explanation:
In hypothesis testing, we typically begin with a null hypothesis (Ho) and an alternative hypothesis (H₁). The null hypothesis (Ho) represents the assumption that there is no effect or difference, while the alternative hypothesis (H₁) represents the assumption that there is an effect or difference.
In this scenario, your coworker claims that Skittles candy colors come in equal quantities (i.e., the proportion of each color is the same). The null hypothesis reflects this claim, which is that the Skittles come in equal proportions of each color. Therefore, the null hypothesis (Ho) is:
- Ho: Skittles candy colors come in equal quantities.
This means that the proportion of purple Skittles is 1/5, the proportion of green Skittles is 1/5, and so on for all the colors.
On the other hand, your position is that you disagree with your coworker’s claim. Therefore, you are proposing that the proportions of the different colors are not equal. This represents the alternative hypothesis (H₁), which is:
- H₁: Skittles candy colors do not come in equal quantities.
This hypothesis suggests that the proportions of the different Skittles colors are not equal, meaning that some colors may be more or less frequent than others.
Why other options are incorrect:
- Ho: Red Skittles are cherry flavored; H₁: Red Skittles are strawberry flavored: This hypothesis is about the flavor of Skittles, not about the distribution of colors, so it is irrelevant to the problem.
- Ho:PP; H₁: P1 P2: This is not a valid hypothesis in the context of this problem as it is not clear or specific.
- Ho: Taste the Rainbow; H₁: Do not Taste the Rainbow: This is not related to the proportions of Skittles colors, so it’s not a valid hypothesis.
Statistical Test:
To test the hypothesis at the α = 0.10 level of significance, you would typically use a Chi-square goodness-of-fit test. This test compares the observed frequencies of each color in the sample to the expected frequencies (which, in this case, would be 1/5 of 200 Skittles for each color). If the observed frequencies significantly differ from the expected frequencies, you would reject the null hypothesis.
Let me now display a possible dataset and the test results that you could use for the analysis.
I have displayed the data for the observed and expected frequencies of Skittles colors. You can now use this data to conduct a Chi-square goodness-of-fit test to determine whether the observed frequencies significantly differ from the expected frequencies.