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One sample t-Test
Example

Example of a one sample t-Test

A random sample of 22 fifth grade pupils have a grade point average of 5.0 in maths with a standard deviation of 0.452, whereas marks range from 1 (worst) to 6 (excellent). The grade point average (GPA) of all fifth grade pupils of the last five years is 4.7. Is the GPA of the 22 pupils different from the populations’ GPA?

 

Pupil
Grade points
1
5
2
5.5
3
4.5
4
5
5
5
6
6
7
5
8
5
9
4.5
10
5
11
5
12
4.5
13
4.5
14
5.5
15
4
16
5
17
5
18
5.5
19
4.5
20
5.5
21
5
22
5.5
Mean
5.0
Variance
0.2045

We estimate the standard deviation of the population:

 

and we get the standard deviation of the mean:

 

now we can compute the t-value:

 

 

for the non directed Hypothesis we have a critical t-value of 

for the directed Hypothesis we have a critical t-value of 

 

The obtained t-value is greater that the critical t-value. The grade point average of the 22 pupils is different from the populations’ GPA.

 

BrightStat Output of this example

 

This is a fictitious example. 






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