Manual formula for one sample t-test

A psychologist makes use of a test instrument for measuring depression. The instrument is known to have a mean score of 70 for normal individuals. Twenty individuals who have been described as severely depressed by a therapist takes the tests. A psychologist is interested to know if the average test score made by severely depressed individuals is greater than 70. The data are reflected on the table below. Scores Made by Severely Depressed Individuals No. Score No. Score ERSI 75 11 75 77 12 74 73 13 63 80 14 76 65 15 67 74 16 70 75 17 69 69 18 76 71 19 65 10 72 20 68