Statistical tests can be either one or two-sided, and this is important for finding the critical value of a test. Below are three possible null and alternative hypotheses for a single sample mean test. Given the same alpha, each of the three tests would have a different critical value (or values).
Warning Signs of Osteoarthritis. 1  Pain and stiffness in a joint after getting out of bed or sitting for long. 2  Swelling in one or more joints, especially those at the ends of the fingers (closest to the nail), thumbs, neck, lower back, knees, and hips. 3  Crunching feeling or the sound of bone rubbing on bone.
Symptoms of osteoarthritis most often develop gradually and include: 1  Joint aching and soreness, especially with movement. 2  Pain after overuse or after long periods of inactivity. 3  Stiffness after periods of rest. 4  Bony enlargements in the middle and end joints of the fingers (which may or may not be painful). 5  Joint swelling.