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.


When the test statistic for the chi-square independence test is large, you will, in most cases, reject the null hypothesis.

Verified step by step guidance

1. Understand the context: The chi-square independence test is used to determine whether two categorical variables are independent. The null hypothesis (H₀) states that the variables are independent, while the alternative hypothesis (H₁) states that they are not independent.
2. Recall the relationship between the test statistic and the null hypothesis: A large test statistic indicates a greater deviation from the expected frequencies under the null hypothesis, suggesting that the observed data does not align well with the assumption of independence.
3. Review the decision rule: In hypothesis testing, if the test statistic is large enough to exceed the critical value (determined by the chi-square distribution and the significance level, α), you reject the null hypothesis.
4. Evaluate the statement: The statement is true because a large test statistic typically leads to rejecting the null hypothesis, as it implies strong evidence against the assumption of independence.
5. If the statement were false, the correction would be: 'When the test statistic for the chi-square independence test is large, you will, in most cases, fail to reject the null hypothesis.' However, this is incorrect based on the logic of the test.

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 in each category to the frequencies expected under the null hypothesis of independence. A large test statistic indicates that the observed data significantly deviates from what would be expected if the variables were independent.

Null Hypothesis

The null hypothesis is a statement that assumes no effect or no association between variables in a statistical test. In the context of the chi-square independence test, the null hypothesis posits that the two categorical variables are independent of each other. Rejecting the null hypothesis suggests that there is a statistically significant relationship between the variables.

Test Statistic

A test statistic is a standardized value that is calculated from sample data during a hypothesis test. It measures how far the sample statistic is from the null hypothesis, allowing researchers to determine whether to reject or fail to reject the null hypothesis. In the chi-square test, a larger test statistic typically indicates stronger evidence against the null hypothesis.