Chapter 11.2, Problem 54E

a)

To determine

To state the null and alternative hypotheses.

Answer to Problem 54E

  $H_0$ : There is no difference in the proportion of people who support the death penalty of the educational categories.

  $H_a$ : There is a difference in the proportion of people who support the death penalty of the educational categories.

Explanation of Solution

Given:

Calculation:

The null and alternative hypotheses:

  $H_0$ : There is no difference in the proportion of people who support the death penalty of the educational categories.

  $H_a$ : There is a difference in the proportion of people who support the death penalty of the educational categories.

b)

To determine

To state the conclusion.

Answer to Problem 54E

There is convincing evidence that there is a difference in the proportion of people who support the death penalty of the educational categories.

Explanation of Solution

Given:

Calculation:

The p-value = 0.000. Therefore, we can say, there is very less chance of obtaining the sample results or more extreme when there is a no difference in the proportion of people who support the death penalty of the educational categories.

Decision: P-value < 0.05, reject H0.

Conclusion: There is convincing evidence that there is a difference in the proportion of people who support the death penalty of the educational categories.

c)

To determine

To compare chi-square test and z-test.

Answer to Problem 54E

The p-value of chi-square test and z-test is same so, conclusion based on two tests are same.

Explanation of Solution

Given:

Calculation:

The p-value = 0.000. The p-value of chi-square test and z-test is same. Therefore, conclusion based on two tests are same.

Decision: P-value < 0.05, reject H0.

Also, chi-square test statistic =17.590 and z-test statistic = 4.19

We know the property that square of z becomes the chi-square.

So, $z^2={\left(4.19\right)}^2=\text{ 17}\text{.590}={\chi }^2$

This property is satisfied.