A psychologist develops a new inventory to evaluate depression. Using a very large standardization group of "normal" individuals, the mean score on this test is u=55 with o=12, and the scores are normally distributed. To determine if the test is sensitive in detecting those individuals that are severely depressed, a random sample of patients who are described as depressed by a therapist is selected and given the test. Presumably, the higher the score on the inventory is, the more depressed the patient is. The data are as follows: 59, 60, 60, 67, 65, 90, 89, 73, 74, 81, 71, 71, 83, 83, 88, 83, 84, 86, 85, 78, 79. Do patients score significantly differently on the test? Test with the .01 level of significance for two tails.
State the null and alternate hypothesis. Show it in symbols.