Chapter 19, Problem 36E

(a)

To determine

To explain why the poll is actually inconclusive.

Explanation of Solution

It is given in the question that a TV news reporter says that a proposed constitutional amendment is likely to win approval in the upcoming election because a poll of $1505$ likely voters indicated that $52\%$ would vote in favor. Thus, the poll is actually inconclusive because $50\%$ approval falls within the margin of error of $3\%$ . If $50\%$ of people favor the amendment then that means that people do not heavily favor it.

(b)

To determine

To find out what confidence level did the pollsters use.

Answer to Problem 36E

Confidence interval is $98\%$ .

Explanation of Solution

It is given in the question that a TV news reporter says that a proposed constitutional amendment is likely to win approval in the upcoming election because a poll of $1505$ likely voters indicated that $52\%$ would vote in favor. Thus, to find what confidence level did the pollsters use, we have,

  $\begin{array}{l}0.03=z^{*}\times \sqrt{\frac{0.52\times 0.48}{1505}}\\ \text{Solve for }{z}^{*}\\ \Rightarrow z^{*}=\frac{1}{0.03}\times \sqrt{\frac{0.52\times 0.48}{1505}}\\ \Rightarrow z^{*}=2.330\\ \text{So, confidence interval}=98\%\end{array}$

Thus, $98\%$ confidence level did the pollsters use.