Final answer:
The main answer concerns calculating the F statistic from the given variances of two college instructors' grades to test if there's a significant difference, and using the p-value to compare with the significance level for a conclusion.
Step-by-step explanation:
If the variance of a variable is 169, it implies that the spread of data points around the mean is quantified by this variance value. The variance is the square of the standard deviation, a measure of dispersion in a data set. Additionally, understanding variance is essential when conducting statistical tests such as comparing variances between groups to establish if there is a significant difference in the data sets as indicated in the scenario of college instructors grading exams differently.In the example provided, the question pertains to testing the claim that the first instructor's variance in grades is smaller than the second's. This involves using statistical methods such as the F-test to compare variances. It is important to note that the F-test requires assumptions such as the normality of data and equality of sample sizes. The conclusion of such a test is based on the comparison of a calculated F statistic to a critical value at a certain level of significance, determining whether to reject or retain the null hypothesis.To summarize, the main answer to the question would involve calculating the F statistic using the variances provided and determining the p-value to compare with the significance level. Based on this, a conclusion regarding the claim about the instructors' grading variances can be made.