Thi is a question that we were suppose find the equation to answer the question but I am not sure how to figure out how to determine the equation that should be used. Here is the question and answer:
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.
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?
random sample 36
confidence interval .95
6/sq rt 36
80 + (1.960) 6/sq rt 36=81.96
80 - (1.960) 6/sq rt 36=78.04
Yes I would say the students are smarter than the year before because the lowest limit of the 95% confidence interval would be 78.04 which would be 2.04 more points. However it could be due to a smarter than average student, rather than a group of students.
80 + (1.960) 6/sq rt 16=82.94
80 - (1.960) 6/sq rt 16=77.06
However, this may not be normal because of the smaller class size.
Another thing, where the heck did 1.960 come from?
Thanks for all your help!