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The type of test you would use to test whether the Skittles follow their stated distribution is the **Goodness of Fit** test. 

This is because:
- The company claims that the Skittles colors are evenly distributed, which implies a specific expected distribution (equal proportions).
- The student is comparing the observed counts from the sample with these expected counts.
- The Goodness of Fit test, specifically the Chi-Square Goodness of Fit test, is used to compare observed frequencies to expected frequencies for categorical data.

Would you like a deeper explanation on how the Goodness of Fit test works or the next steps for solving this? 

### Follow-up questions:
1. How do you calculate expected frequencies for the Goodness of Fit test?
2. What are the degrees of freedom in a Goodness of Fit test?
3. How do you compute the Chi-Square statistic for this problem?
4. What conditions must be met to apply the Chi-Square Goodness of Fit test?
5. How does the Goodness of Fit test differ from the Test for Independence?

**Tip**: In a Goodness of Fit test, the null hypothesis is that the observed frequencies match the expected frequencies, while the alternative hypothesis suggests they do not.

A student wanted to know if Skittles follow their stated distribution. The company claims that they distribute all 5 colors evenly. The student takes a random sample of 500 Skittles and finds the following distribution: Green (75), Yellow (105), Orange (110), Red (115), Purple (90). What type of test would you use to test if Skittles follow their stated distribution?

This problem involves using the Chi-Square Goodness of Fit test to determine if the color distribution of Skittles follows the company's claim of equal proportions. The observed frequencies of five colors in a sample of 500 Skittles are compared to the expected even distribution.

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