Final answer:
The main idea is that vanilla is the most popular ice cream flavor among Americans. A chi-square test of independence determines if there is a significant association between geographic location and ice cream flavor preference at a 5 percent significance level.
Step-by-step explanation:
The main idea of the sentence is that vanilla is the most preferred ice cream flavor among Americans, followed by a few other popular choices. In statistical terms, to analyze whether geographic location is independent of ice cream flavor preference, a chi-square test of independence would be used.
This test evaluates whether there is a significant association between the two categorical variables (geographic location and ice cream flavor preference) based on the observed frequencies in each category.
To perform this test at a 5 percent significance level, one would compare the calculated chi-square test statistic to the critical value from the chi-square distribution with the appropriate degrees of freedom. If the test statistic exceeds the critical value, we would reject the null hypothesis that geographic location and ice cream flavor preference are independent, suggesting there is a significant association between them.