Final answer:
The smallest value of k that ensures a k-NN classifier predicts 'Berkeley' as the class is 24, which is one more than the total Stanford student rows.
Step-by-step explanation:
The question pertains to a machine learning technique called k-Nearest Neighbors (k-NN). In the given scenario, to ensure that a k-NN classifier always predicts 'Berkeley' as the class, you would need to choose a value of k that is larger than the number of rows of Stanford students in the training set.
Since there are 23 rows of Stanford students, the smallest k value that would ensure 'Berkeley' is always the predicted class is 24 (which is one more than the number of Stanford students), assuming there are no ties to resolve.