Final answer:
Favorable and unfavorable variances can be misleading and do not solely indicate good or bad performance in business or education, such as grading consistency among college instructors.
Step-by-step explanation:
The statement that favorable and unfavorable variances are not necessarily indicators of good or bad performance is generally true. Variance in a business context refers to the difference between what was expected, or budgeted, and the actual result. A favorable variance indicates a better-than-expected outcome, while an unfavorable variance suggests a worse-than-expected result. However, these variances may not accurately reflect performance. For example, a favorable variance could result from suboptimal conditions such as reduced quality or altered standards. Conversely, an unfavorable variance might be a result of investment in quality or other strategic decisions that could benefit the business in the long term.
Considering the example given, comparing the variance of grades between two instructors, one with a variance of 52.3 and the other with 89.9, does not inherently indicate which instructor graded 'better' or 'worse.' Instead, the focus is on consistency and calibration of grading standards. A test of hypothesis could be applied using an F-test to check if there is a significant difference between the two instructors' variances, with a level of significance set at 10 percent, to ensure the comparability of grading across instructors.