Chapter PI, Problem 30RE

(a)

To determine

To find out what is the marginal distribution of majors.

Answer to Problem 30RE

  $\begin{array}{l}\text{Maths/science}=25.56\%\\ \text{Agriculture}=41.7\%\\ \text{Humanities}=19.28\%\\ \text{Others}=13.45\%\end{array}$

Explanation of Solution

In the question, researchers want to find out is your birth order related to your choice of major. Thus the table related to it is given in the question which shows the birth order and the major of subjects. Thus, the marginal distribution of majors can be calculated as:

  $\begin{array}{l}\text{Maths/science}=\frac{57}{223}\\ =0.2556\\ =25.56\%\\ \text{Agriculture}=\frac{93}{223}\\ =0.4170\\ =41.7\%\\ \text{Humanities}=\frac{43}{223}\\ =0.1928\\ =19.28\%\\ \text{Others}=\frac{30}{223}\\ =0.1345\\ =13.45\%\end{array}$

(b)

To determine

To find out what is the conditional distribution of majors for oldest children.

Answer to Problem 30RE

  $\begin{array}{l}\text{Maths/science}=30.09\%\\ \text{Agriculture}=42.06\%\\ \text{Humanities}=13.27\%\\ \text{Others}=10.62\%\end{array}$

Explanation of Solution

In the question, researchers want to find out is your birth order related to your choice of major. Thus the table related to it is given in the question which shows the birth order and the major of subjects. Thus, the conditional distribution of majors for oldest children can be calculated as:

  $\begin{array}{l}\text{Maths/science}=\frac{34}{113}\\ =0.3009\\ =30.09\%\\ \text{Agriculture}=\frac{52}{113}\\ =0.4206\\ =42.06\%\\ \text{Humanities}=\frac{15}{113}\\ =0.1327\\ =13.27\%\\ \text{Others}=\frac{12}{113}\\ =0.1062\\ =10.62\%\end{array}$

(c)

To determine

To find out what is the conditional distribution of majors for the children born second.

Answer to Problem 30RE

  $\begin{array}{l}\text{Maths/science}=20.29\%\\ \text{Agriculture}=39.13\%\\ \text{Humanities}=24.64\%\\ \text{Others}=15.94\%\end{array}$

Explanation of Solution

In the question, researchers want to find out is your birth order related to your choice of major. Thus the table related to it is given in the question which shows the birth order and the major of subjects. Thus, the conditional distribution of majors for the children born second can be calculated as:

  $\begin{array}{l}\text{Maths/science}=\frac{14}{69}\\ =0.2029\\ =20.29\%\\ \text{Agriculture}=\frac{27}{69}\\ =0.3913\\ =39.13\%\\ \text{Humanities}=\frac{17}{69}\\ =0.2464\\ =24.64\%\\ \text{Others}=\frac{11}{69}\\ =0.1594\\ =15.94\%\end{array}$

(d)

To determine

To explain do you think that the college major appears to be independent of birth order.

Answer to Problem 30RE

Yes, we think that the college major appears to be independent of birth order.

Explanation of Solution

In the question, researchers want to find out is your birth order related to your choice of major. Thus the table related to it is given in the question which shows the birth order and the major of subjects. Thus, yes, we think that the college major appears to be independent of birth order because college majors seem to be independent of birth order. The only real changes are $10\%$ changes from first to second children in the Math/science categories and humanities but even those are negligible.