Final answer:
The diagnostic test for hip and back pain along with stiffness that improves with activity over the course of the day and worsens at rest is 4) Physical examination.
Step-by-step explanation:
This is because during a physical examination, a healthcare professional can assess the range of motion, strength, and tenderness in the hip and back. They may also perform specific maneuvers to further evaluate the condition, such as assessing for the presence of sciatica or performing a straight leg raise test to evaluate for nerve impingement.
X-ray and MRI imaging can be helpful in ruling out other underlying causes of the pain, but they may not be able to provide a definitive diagnosis for the specific symptoms mentioned. Blood tests, on the other hand, can be useful in identifying certain underlying conditions that may cause joint pain, but they may not directly diagnose the cause of hip and back pain. Therefore the correct answer is 4) Physical examination.