Final answer:
The statement is true; variances between actual and budgeted amounts provide management with insights into an organization's performance. Tools like the chi-square test and F test help in assessing and comparing variances for better decision-making.
Step-by-step explanation:
The statement is TRUE: Variances between actual and budgeted amounts do indeed inform management about performance relative to the budget. When an organization creates a budget, it sets expectations for revenues and expenses over a certain period.
After that period, management will often compare the actual amounts incurred or earned against the budgeted amounts to understand how the organization is performing. These variances can illuminate areas of operational efficiency or inefficiency, signaling where adjustments might be necessary. Test of a Single Variance, the chi-square test may be applied to determine if the observed variance is significantly different from the expected variance, thereby identifying significant deviations.
Additionally, the 13.4 Test of Two Variances, such as comparing the variances of grades assigned by different instructors, will require certain assumptions to be true to perform an F test. For example, the samples must be independent, and the populations must be normally distributed. Example 13.5 shows how one might test whether there is significant variability in grading between two instructors, which is relevant for assessing consistency in academic performance assessment.
Variance analysis, thus, is a critical tool for management in both financial and operational decision-making, as indicated in the examples provided using budget variance and grading variance.