A psychology professor who taught a very large lecture class wanted to test whether the students who turned in tests early scored differently from the overall mean on the test. The overall mean score on the test was 76 with a standard deviation of 22. The mean score for the first 100 students to turn in tests was 81.5.

(i) Would the professor use a one-tailed or a two-tailed test:

(ii) What is the probability that he would obtain his result due to chance (answer with 4 decimal places):

(iii) What is the statistical conclusion the professor should reach at the 0.05 level:

(iv) Compute the 60% confidence interval limits: Lower and Upper