# Thread: How did they determine . . .

1. ## How did they determine . . .

Hey everyone,

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?

sd 6
random sample 36
mean 80
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?

2. Originally Posted by foofergutierrez
Hey everyone,

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?

sd 6
random sample 36
mean 80
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?