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.
Here are some common signs of osteoarthritis that may help you to identify and better describe your pain to your doctor: 1  Pain that aches deep into the joint. 2  Pain that feels better with rest. 3  Pain that isn't noticeable in the morning, but gets worse throughout the day. 4  Pain that radiates into your buttocks, thighs, or groin.