True or False? In Exercises 5 and 6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.


If the two variables in a chi-square independence test are dependent, then you can expect little difference between the observed frequencies and the expected frequencies.

Verified step by step guidance

1. Understand the context of the chi-square independence test: This test is used to determine whether two categorical variables are independent or dependent. Independence means the variables do not influence each other, while dependence means they are related.
2. Recall the relationship between observed and expected frequencies: In a chi-square test, the observed frequencies are the actual counts from the data, and the expected frequencies are the counts predicted under the assumption of independence.
3. Analyze the statement: If the two variables are dependent, it implies that the observed frequencies will differ significantly from the expected frequencies. This is because dependence indicates a relationship that deviates from the assumption of independence.
4. Identify the error in the statement: The statement claims that if the variables are dependent, there will be little difference between observed and expected frequencies. This is false because dependence typically results in larger differences between observed and expected frequencies.
5. Rewrite the statement as true: If the two variables in a chi-square independence test are dependent, then you can expect significant differences between the observed frequencies and the expected frequencies.

Key Concepts

Chi-Square Independence Test

The chi-square independence test is a statistical method used to determine if there is a significant association between two categorical variables. It compares the observed frequencies of occurrences in each category to the expected frequencies, which are calculated under the assumption that the variables are independent. A significant difference suggests that the variables are related.

Observed vs. Expected Frequencies

Observed frequencies are the actual counts collected from data, while expected frequencies are the counts we would expect if there were no association between the variables. In a chi-square test, if the variables are independent, the observed and expected frequencies should be similar. A large discrepancy indicates a potential dependence between the variables.

Dependence of Variables

When two variables are dependent, the value of one variable affects or is related to the value of the other. In the context of a chi-square test, if the variables are dependent, we would expect significant differences between observed and expected frequencies, indicating that the distribution of one variable changes based on the level of the other variable.