Chapter 11.2, Problem 28E

a.

To determine

To explain: The conditional distribution of responses for each group of parents.

Explanation of Solution

Given:

The data set is:

	Black Parents ( B )	Hispanic Parents ( H )	White Parents ( W )
Excellent	12	34	22
Good	69	55	81
Fair	75	61	60
Poor	24	24	24
Don’t know	22	28	14
Total	202	202	201

Formula used:

  $\text{Probability}\left(p\right)=\frac{\text{Number of favourable}}{\text{Total number of exhaustive}}$

Calculation:

The conditional distribution of response for each group of parents, can be calculated as:

  $\begin{array}{c}\text{P}\left(E|B\right)=\frac{\frac{\text{n}\left(E\cap B\right)}{n}}{\frac{n\left(B\right)}{n}}\\ =\frac{12}{202}\\ =0.0594\end{array}$

Similarly, for all,

	Black Parents	Hispanic Parents	White Parents
Excellent	0.0594	0.1683	0.1095
Good	0.3416	0.2723	0.4030
Fair	0.3713	0.3020	0.2985
Poor	0.1188	0.1188	0.1194
Don’t know	0.1089	0.1386	0.0697

b.

To determine

To construct: The graph to comparing the conditional distribution in part (a).

Explanation of Solution

Graph:

Graph for the given data, it could be construct as:

  

Interpretation:

The probability distribution of White parents, seems that symmetric distribution.

c.

To determine

To explain: Comparing the conditional distribution of response for the three group of parents.

Explanation of Solution

Most of the parents having a fair opinion of the schools. The parents of Hispanic, they have same opinion for both Poor and Don’t know.

The Hight of good bar in which, which is higher than both black and Hispanic.