Chapter 21, Problem 11E

(a)

To determine

To make a $95\%$ confidence interval for his approval rating by all U.S. adults.

Answer to Problem 11E

  $(0.274,0.327)$ .

Explanation of Solution

It is given in the question that in May George Bush’s approval rating stood at $30\%$ according to a CBS News/New York times. Thus, we have,

Let us first check the conditions for the following as:

Random condition: It is satisfied as it is assumed that the sample is randomly selected.

Normal condition: It is satisfied as,

  $\begin{array}{l}np=338>10\\ n(1-p)=787>10\end{array}$

$10\%$ condition: It is satisfied as the sample size is less than $10\%$ of the population size.

Thus, all the conditions are met. Therefore, now, to find the confidence interval we will use the calculator $\text{TI}-89$ . So, we have to first go to the $\text{Ints}$ menu and select $5:1-\text{PropZInt}$ . Then we have to enter the number of successes observed and the sample size. Then specify a confidence level. Then the interval will be calculated. Thus, we have,

  $\begin{array}{l}x=338\\ n=1125\\ c=0.95\end{array}$

Thus, the confidence interval will be as:

  $(0.274,0.327)$

(b)

To determine

To test the null hypothesis that Bush’s approval rating was no better than the $27\%$ level established by Richard Nixon during the Watergate Scandal.

Answer to Problem 11E

The null hypothesis is rejected.

Explanation of Solution

It is given in the question that in May George Bush’s approval rating stood at $30\%$ according to a CBS News/New York times. Thus, the confidence interval will be as:

  $(0.274,0.327)$

Thus, since $0.27$ is not within the confidence interval calculated in part (a), we reject the hypothesis that $p=0.27$ .