# 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?

Thanks for all your help!

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?

Thanks for all your help!
The 1.960 comes from using the z-statistic. But since you don't know the standard deviation of the population you have to use the t-statistic (with 35 degrees of freedom). n = 36 is large enough that you don't have to worry too much about normality (the person who set the question thinks this, anyway).

3. what is the z-statistic?

4. Originally Posted by foofergutierrez
what is the z-statistic?
Level of Significance of a Test: the Z statistic

Have you been taught how to construct a confidence interval or are you just plugging numbers into a black box?

5. Basically just plugging. Its been since Feb since I have used any of this so I have no idea what I am doing and the book really does not help. I am a total mess with this course and its only the first week leaving 4 more weeks of torture.