Q. 28 - The Practice of Statistics for AP

Question

The nonprofit group Public Agenda conducted telephone interviews with three randomly selected groups of parents of high school children. There were $202$ black parents, $202$ Hispanic parents, and $201$ white parents. One question asked was “Are the high schools in your state doing an excellent, good, fair, or poor job, or don’t you know enough to say?” Here are the survey results:

(a) Calculate the conditional distribution (in proportions) of responses for each group of parents. 

(b) Make an appropriate graph for comparing the conditional distributions in part (a). 

(c) Write a few sentences comparing the distributions of responses for the three groups of parents 

Step-by-Step Solution

Answer

(a) 

(b) 

(c) The majority of parents have a favourable or balanced assessment of their children's high schools.

Hispanic parents believe that high school is the best and that they know the least.

In each category, the proportion of Poor opinions is nearly the same.

Part (a) Step 1: Given information

The given data is 

Part (a) Step 2: Explanation

We have to use the formula of probability:

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

For each group of parents, the conditional distribution of response can be determined as follows:

$$\begin{gathered} \mathrm{P}(E\mid B)=\frac{\frac{\mathrm{n}(E\cap N)}{n}}{\frac{n\left(B\right)}{n}} \\ =\frac{12}{202} \\ =0.0594 \end{gathered}$$

We may carry out this technique in the same way for all of them.

Part (b) Step 1: Given information

The given data is 

Part (b) Step 2: Explanation

Let's make a comparison histogram.

The conditional probability computed in the exercise $28$ must have the same width and height for all bars.

Part (c) Step 1: Given information

The given data is 

Part (c) Step 2: Explanation

From Part 2 of the graph (b)

The majority of parents have a favourable or balanced assessment of their children's high schools.

Hispanic parents believe that high school is the best and that they know the least.

In each category, the proportion of Poor opinions is nearly the same.