A medical doctor uses a diagnostic test to determine whether a patient has arthritis. A treatment will be prescribed only if the doctor thinks the patient has arthritis. The situation is similar to using a null and an alternative hypothesis to decide whether to prescribe the treatment. The hypotheses might be stated as follows.

• \(H_0\) : The patient does not have arthritis.
• \(H_a\) : The patient has arthritis.

Which of the following represents a Type II error for the hypotheses?

In a Type II error, the alternative hypothesis is actually correct but the null hypothesis is accepted.