Six Sigma Black Belt Certified Practice Exam 2026 - Free Six Sigma Practice Questions and Study Guide

The chi-square (χ²) value and degrees of freedom (df) relate to how a statistical test evaluates the differences between observed and expected frequencies in categorical data. In the context of a fail-safe device, the chi-square value quantifies how well the observed results fit a theoretical model.

The chi-square statistic is calculated based on the differences between observed and expected frequencies, and it provides a measure of how much deviation exists between them. A higher χ² value suggests that the observed data does not fit the expected data well, while a lower value indicates a better fit. In this case, the calculated chi-square value of 57.5 indicates specific discrepancies in the test results of the fail-safe device.

Degrees of freedom, on the other hand, depend on the number of categories in the study minus one (and sometimes minus the number of parameters estimated). In this scenario, having four degrees of freedom means that there are a total of five categories being evaluated in the device's performance or results.

The combination of a χ² value of 57.5 and degrees of freedom of 4 provides a comprehensive view of how the fail-safe device performed compared to expected outcomes. This information enables better assessments of the device's reliability and effectiveness in real-world scenarios