Six Sigma Green Belt Certification Practice Exam

When evaluating police dogs using a chi-squared test, what is the critical value (X-squared) at a 95% confidence interval?

1. 0.352

2. 5.99

3. 7.81

4. 0.1026

The correct answer is: 7.81

When conducting a chi-squared test, the critical value is determined based on the significance level and the degrees of freedom associated with the data. In this case, for a 95% confidence interval (or a 5% significance level), the critical value allows researchers to discern whether to reject the null hypothesis. Generally, the degrees of freedom for a chi-squared test can be calculated as the number of categories minus one, which will influence the critical value. For many common scenarios, especially with two categories or groups, the critical value for 95% confidence level is typically around 5.99, and as the degrees of freedom increase, the critical value also increases. However, for a classic chi-squared distribution table, the value 7.81 represents the threshold for 3 degrees of freedom at the 0.05 significance level. In this particular scenario, since 7.81 aligns with standard calculations for a chi-squared distribution when the degrees of freedom are two or three, this critical value indicates the threshold to determine if the observed frequencies deviate significantly from the expected frequencies due to random chance. Understanding that the correct choice represents the appropriate response based on the confidence interval context is crucial in evaluating statistical results. Such critical values provide