Six Sigma Black Belt Certified Practice Exam

Based on a contingency table for an organization, what is the expected number of oil changes for Station 1?

1. 70

2. 76

3. 80

4. 100

The correct answer is: 80

To determine the expected number of oil changes for Station 1 using a contingency table, we apply the principle of expected frequencies in a chi-square test or similar statistical analyses. The expected frequency for a certain category (like Station 1) is usually calculated based on the total outcomes and the relative proportions of that category to the overall sample. In a typical contingency table, you sum the totals of the rows and columns to find the overall total, then use the formula: Expected Frequency = (Row Total * Column Total) / Grand Total By inserting the respective totals into this formula, one can derive the expected number of oil changes specifically assigned to Station 1. If the correct calculation leads to the value of 80, which corresponds to option C, this indicates that based on the data provided in the contingency table, Station 1 is expected to handle a certain proportion of oil changes that rounds to 80 when considering the total number of oil changes across stations and their respective proportions. Understanding this calculation is crucial for properly interpreting data from a contingency table. It provides insight into how each station is performing relative to its expected role within the overall operation, which can assist in identifying any discrepancies or areas for improvement in service delivery.