Step 1 :The problem asks for the sample standard deviation of the paired differences. This means we need to calculate the difference between the number of sit-ups before and after the course for each individual, and then calculate the standard deviation of these differences.
Step 2 :First, we list the number of sit-ups each individual could do before the course: \(42, 42, 23, 32, 30, 42, 25, 47, 35, 38\).
Step 3 :Next, we list the number of sit-ups each individual could do after the course: \(57, 48, 29, 41, 36, 57, 40, 51, 41, 40\).
Step 4 :We then calculate the difference between the number of sit-ups before and after the course for each individual, resulting in the following list: \(15, 6, 6, 9, 6, 15, 15, 4, 6, 2\).
Step 5 :Finally, we calculate the sample standard deviation of these differences, which is approximately \(4.880801\).
Step 6 :Final Answer: The sample standard deviation of the paired differences is \(\boxed{4.880801}\).