Question
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According to a recent survey of 1410 voters, feel that the president is doing an acceptable job.
Construct a confidence interval to estimate the proportion of voters who feel the president is doing a
acceptable job.



Margin of Error:
Wetween (round to decimal places)
benfident that the proportion of voters who feel the president is doing an acceptable job is

Ask by Lane Hobbs. in the United States
Jan 22,2025

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Tutor-Verified Answer

Answer

We are 93% confident that between 69.83% and 74.17% of voters feel the president is doing an acceptable job.

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Beyond the Answer

To construct a confidence interval for the proportion of voters who believe the president is doing an acceptable job, let’s break it down step by step using the survey data provided.
  1. Sample proportion :
    Given that of voters feel the president is doing an acceptable job, we have:
  2. Value of :
    For a confidence level, . Thus:
  3. Critical value :
    To find , we look for the z-value that corresponds to the cumulative probability of . From a standard normal (Z) table or calculator, we find:
  4. Margin of Error :
    The formula for the margin of error is given by:
    Substituting in the values:
  5. Confidence Interval:
    The confidence interval is given by:
    Thus:
So, rounding to 43 decimal places, the confidence interval for the proportion of voters who feel the president is doing an acceptable job is approximately:
In conclusion, we can say that we are confident that the proportion of voters who feel the president is doing an acceptable job lies within this range!

Related Questions

\begin{tabular}{l} ter 13 Review \\ \( 1 \leftarrow \quad \begin{array}{l}\text { A Morning Consult/Politico poll of } 1997 \text { registered voters in July } 2020 \text { asked a standard polling question of whether the United States was headed in the "Right Direction" or } \\ \text { was on the "Wrong Track." } 75.3 \% \text { said that things are on the wrong track vs. } 24.7 \% \text { who said "right direction." Complete parts a and b. } 51.35 \%, 19 \text { of } 37 \text { points } \\ \text { Part } 1 \text { of 2 }\end{array} \) \\ \( \begin{array}{l}\text { a) Calculate the margin of error for the proportion of all U.S. adults who think things are on the wrong track for } 99 \% \text { confidence. } \\ \text { ME }=\square \text { (Round to three decimal places as needed.) }\end{array} \) \\ \hline\end{tabular}

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