Chapter 21, Problem 9E

(a)

To determine

To estimate the percentage of all American males who measure success primarily from their work and use a $98\%$ confidence interval and check the condition.

Answer to Problem 9E

  $(0.019,0.041)$ .

Explanation of Solution

It is given in the question that time magazine reported the results of a random telephone poll commissioned by the spike network. 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,

  $\begin{array}{l}np=39>10\\ n(1-p)=1263>10\end{array}$

$10\%$ 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,

  $\begin{array}{l}x=39\\ n=1302\\ c=0.98\end{array}$

Thus, the confidence interval will be as:

  $(0.019,0.041)$

(b)

To determine

To explain what does your confidence interval indicate.

Explanation of Solution

It is given in the question that time magazine reported the results of a random telephone poll commissioned by the spike network. Thus, the confidence interval will be as:

  $(0.019,0.041)$

Thus, our confidence interval indicate that since $5\%$ is not in the interval there is an evidence that fewer than $5\%$ of all men use work as their primary measure of success.

(c)

To determine

To find out what is the level of significance of this test.

Answer to Problem 9E

  $\alpha =0.01$ .

Explanation of Solution

It is given in the question that time magazine reported the results of a random telephone poll commissioned by the spike network. Thus, the confidence interval will be as:

  $(0.019,0.041)$

Thus, our confidence interval indicate that since $5\%$ is not in the interval there is an evidence that fewer than $5\%$ of all men use work as their primary measure of success. Thus, this is a lower tail test based on a $98\%$ confidence interval thus, then $\alpha =0.01$ .