Final answer:
When comparing the grading variances between two college instructors, an F-test for two variances can be used to test if one has a smaller variance. The null hypothesis typically states no difference, and the alternative hypothesis reflects the specific claim. The provided example concludes the first instructor has a significantly smaller variance at the 10 percent significance level.
Step-by-step explanation:
Facility-related standards deal with ensuring consistent quality and operations within a physical space, such as a classroom, laboratory, or any other place where activities are conducted. They are part of a broader set of standards that might include safety, accessibility, and function-specific requirements. When analyzing facility-related standards in the context of grading variances, these standards can be especially relevant in situations where the physical environment may impact the assessment process or outcomes.
In the example provided, two college instructors are comparing the variance in grades they assigned to the same set of math exams. The first instructor's grades have a variance of 52.3, while the second's grades have a variance of 89.9. To test the claim that the first instructor's variance is smaller, we can use an F-test for two variances. The null hypothesis in this scenario would be that there is no difference between the two variances, while the alternative hypothesis is that there is a difference, and specifically that the first instructor's variance is smaller.
When conducting an F-test, certain assumptions must be met, such as the samples being drawn from normally distributed populations, independence of samples, and equal variances. It is important to validate these assumptions, as violations may necessitate further statistical testing or alternative methods of analysis. As outcomes from the example conclude, there is sufficient evidence at the 10 percent level of significance to support the claim that the first instructor's variance in grades is smaller.