Chapter 14, Problem 1CQ

Exercises 1-4 refer to the following data:

At a certain college: random samples of students with various majors were taken, and their grade point averages (GPA) were computed. The following table presents the sample means, standard deviations, and sample sizes.

How many degrees of freedom are there for SSTr and for SSE?

To determine

Tofind : The number of degree of freedom for $SSTr$ and $SSE$ .

Answer to Problem 1CQ

The number of degree of freedom for $SSTr$ and $SSE$ are $3$ and $194$ respectively.

Explanation of Solution

Given information :

The data is shown below.

Major	Mean	Standard Deviation	Sample Size
English	3.15	0.45	50
Statistics	3.05	0.56	48
Psychology	3.19	0.35	45
Business	3.01	0.49	55

Calculations:

From the given data the number of sample $I=4$ .

The total sample size is given as,

  $N=n_1+n_2+n_3+n_4$

Substitute the values from the table.

  $\begin{array}{c}N=50+48+45+55\\ =198\end{array}$

The degree of freedom for $SSTr$ is,

  $\begin{array}{c}dof=I-1\\ =4-1\\ =3\end{array}$

The degree of freedom for $SSE$ is,

  $\begin{array}{c}dof=N-I\\ =198-4\\ =194\end{array}$

Therefore, the number of degree of freedom for $SSTr$ and $SSE$ are $3$ and $194$ respectively.