Hypothesis Testing - Statistics

Here the scenario:

Over many years of administering tests to my statistics students I have found that the overall average of the scores on the first exam that I give each semester is 76.

Use the attachment to answer these questions.

Well, this semester my class (36 of them -- assume this is a sample) scored an average score of 80 on the exam (standard deviation was 6).  At the .05 level of significance, is this class smarter than the classes I usually have?

1.  Show me the test you would conduct to answer the question above.  List all five steps and make sure we can all see how you arrived at your answer.  (Try this on you own -- this isn't a test and if you are not correct then this is a great time to find out why!  Then compare your response to the others' responses.)

2.  What changes in your test if the class size was only 16 (show the test)?  Why?  Show the 5 steps of the test under the assumption of the sample size of 16 instead of the larger sample size in number 1.