Chapter 11.2, Problem 49E

a.

To determine

To construct: The appropriate graph that shows the relationship between two variables and interpret it.

Explanation of Solution

Given:

The table is:

Education	Yes	No
Less than high school	58	58
High school graduate	84	129
Some college	169	294
College graduate	98	135
Postgraduate degree	77	99

Calculation:

To construct the graph, the proportions are computed as:

Education	Yes	No
Less than high school	0.5	0.5
High school graduate	0.3944	0.6056
Some college	0.365	0.635
College graduate	0.4206	0.5794
Postgraduate degree	0.4375	0.5625

Graph:

The figure could be constructed as:

  

Interpretation:

From the above figure, it is clear that most of the people in each category are not supporting the law and this proportions seems to be highest in the group of “Some college”

b.

To determine

To check: If the sample is providing sufficient evidence to conclude that the level of education and opinion about a handgun ban are independent or not.

Explanation of Solution

Calculation:

The appropriate null and alternative hypotheses for the provided test could be written as:

  $\begin{array}{l}{H}_0:\text{ Two variables are independent}\\ H_a:\text{ Two variables are dependent}\end{array}$

The expected count is computed as:

Education	Yes	No
Less than high school	46.9409	69.0591
High school graduate	86.1932	126.8068
Some college	187.3589	275.6411
College graduate	94.2864	138.7136
Postgraduate degree	71.2206	104.7794

The test statistic is:

  $\begin{array}{c}{\chi }^2={\displaystyle \sum {\frac{\left(O-E\right)}{E}}^2}\\ =\frac{{\left(58-46.9409\right)}^2}{46.9409}+\frac{{\left(58-69.0591\right)}^2}{69.0591}+\mathrm{.......}+\frac{{\left(99-104.7794\right)}^2}{104.7794}\\ =8.525\end{array}$

The degree of freedom is calculated as:

  $\begin{array}{c}\text{Degree of freedom =}\left(\text{Number of rows - 1}\right)\left(\text{Number of column - 1}\right)\\ =\left(5-1\right)\left(2-1\right)\\ =4\end{array}$

The p-value using chi-square table at 4 degree of freedom is 0.074133

The p -value is above significance level. The null hypothesis does not get rejected. Thus, there is sufficient evidence to conclude that there is not an association between two variables.