Using a chi-square goodness-of-fit test, we can determine if the observed frequency of Skittle flavors in a bag differs significantly from the expected frequency, under the hypothesis that each flavor should be equally represented.
To test M&M Mart Company's claim that each bag of Skittles has the same number of each flavor, we can use a chi-square goodness-of-fit test. To perform the test, we first need to establish the null hypothesis (H0) that each flavor has an equal representation, meaning the expected frequency for each flavor is the total number of Skittles divided by the number of flavors. With five flavors and 50 Skittles in total, we would expect to find 10 of each flavor if the company's claim were true.
Here are the steps for the test:
Calculate the expected frequency for each flavor, which is 10 for this example.
Compute the observed frequencies, which are given as lime 18, lemon 15, orange 3, strawberry 3, grape 11.
Calculate the chi-square test statistic using the formula χ² = Σ((observed - expected)² / expected).
With the level of significance at 0.05, compare the calculated chi-square value to the critical value from the chi-square distribution table with 4 degrees of freedom (the number of categories minus one).
If the calculated chi-square is greater than the critical value, reject the null hypothesis. Otherwise, do not reject the null hypothesis.
The chi-square statistic would inform us whether the observed distribution of flavors significantly differs from the expected distribution. If significant, this suggests the company's claim is not supported.