College

If a researcher reports a [tex]$t$[/tex] statistic with [tex]$df = 18$[/tex], how many individual subjects participated in the experiment?

A. [tex]n = 17[/tex]
B. [tex]n = 18[/tex]
C. cannot be determined from the information given
D. [tex]n = 19[/tex]

Answer :

To determine the number of individual subjects that participated in the experiment based on the given information, we follow these steps:

1. Understanding Degrees of Freedom (df):
- In a t-test involving one sample, the degrees of freedom (df) is calculated as the number of subjects (n) minus 1. This is expressed by the formula:
[tex]\[ df = n - 1 \][/tex]

2. Given Information:
- The problem states that the degrees of freedom (df) is 18.

3. Finding the Number of Subjects (n):
- Since the formula for degrees of freedom is [tex]\( df = n - 1 \)[/tex], we can rearrange this to solve for [tex]\( n \)[/tex] by adding 1 to both sides of the equation:
[tex]\[ n = df + 1 \][/tex]

4. Calculate the Number of Subjects:
- Substitute the given degrees of freedom into the equation:
[tex]\[ n = 18 + 1 = 19 \][/tex]

Therefore, the number of individual subjects that participated in the experiment is [tex]\( n = 19 \)[/tex].