Exploring the Relationship Between Fries Types and Regional Preferences

How can a major food manufacturer analyze if the type of fries sold is dependent on the area of the country?

The major food manufacturer can perform a chi-squared test of independence to assess if the type of fries sold is dependent on the area of the country. This involves collecting sales data, creating a contingency table, calculating the chi-squared statistic, and comparing it to a critical value to decide on rejecting or not rejecting the null hypothesis.

To conduct a test of independence, the major food manufacturer can use a chi-squared test. This statistical test would determine if there is a significant association between two categorical variables - the types of fries sold and the areas of the country. To perform this test, the manufacturer would collect data on the sales of different types of fries across various regions, fill an observed frequency table (contingency table), calculate the expected frequencies, and use the chi-squared formula:

X^2 = ∑((O-E)^2/E)

Where O represents the observed frequency, and E represents the expected frequency. The resulting chi-squared value would then be compared with the critical value from the chi-squared distribution table at the appropriate degrees of freedom to determine if the null hypothesis of independence can be rejected or not. If the calculated value is greater than the critical value, there is evidence to suggest that the type of fries and the area of the country are not independent, indicating that sales might be affected by regional preferences.