Chapter PVI, Problem 21RE

To determine

To construct a $95\%$ confidence interval for the true percentage of American adults who agree with the statement.

Answer to Problem 21RE

We are $95\%$ confident that between the proportion of American adults who would agree with the statement is between $57\%\text{ and 63\%}$ .

Explanation of Solution

It is given in the question that in September, the Harris Poll organization asked $1002$ randomly sampled American adults whether they agreed or disagreed with the following statement given. Thus, to find the confidence interval for proportion we will use the calculator $\text{TI}-89$ . To calculate a confidence interval for a population proportion: Go to the Intsmenu and select $5:1-$ PropZInt. Enter the number of successes observed and the sample size. Specify a confidence level. Calculate the interval. So, we have,

  $\begin{array}{l}n=1002\\ p=0.60\end{array}$

And $\alpha =0.05$ so by using the calculator $\text{TI}-89$ , the confidence interval will be as:

  $(0.57,0.63)$ .

Thus, we are $95\%$ confident that between the proportion of American adults who would agree with the statement is between $57\%\text{ and 63\%}$ .