A Morning Consult/Poiltico poll of 1997 registered voters in July 2020 asked a standard polling question of whether the United States was headed in the “Right Direction” of
was on the “Wrong Track.” said that things are on the wrong track vs. who said "right direction. "Complete parts a and b.
a) Calculate the margin of error for the proportion of all U.S. adults who think things are on the wrong track for confidence.
ME (Round to three decimal places as needed.)
b) Explain what this margin of error means. Select the correct choice below and fill in the answer box within your choice.
(Round to three decimal places as needed.)
A. The probability that any given adult surveyed from the population will respond “Wrong Track” is
B. One is confident that the observed proportion of adults that responded “Wrong Track” is within of the sample proportion.
C. The probability that any given adult surveyed from the sample responded “Wrong Track” is
C. . The .
D. One is confident that the observed proportion of addults that responded “Wrong Track” is within of the population proportion.
D.

Ask by Wood Mills. in the United States

Mar 31,2025

Question

A Morning Consult/Poiltico poll of 1997 registered voters in July 2020 asked a standard polling question of whether the United States was headed in the “Right Direction” of
was on the “Wrong Track.” said that things are on the wrong track vs. who said "right direction. "Complete parts a and b.
a) Calculate the margin of error for the proportion of all U.S. adults who think things are on the wrong track for confidence.
ME (Round to three decimal places as needed.)
b) Explain what this margin of error means. Select the correct choice below and fill in the answer box within your choice.
(Round to three decimal places as needed.)
A. The probability that any given adult surveyed from the population will respond “Wrong Track” is
B. One is confident that the observed proportion of adults that responded “Wrong Track” is within of the sample proportion.
C. The probability that any given adult surveyed from the sample responded “Wrong Track” is
C. . The .
D. One is confident that the observed proportion of addults that responded “Wrong Track” is within of the population proportion.
D.

Ask by Wood Mills. in the United States

Mar 31,2025

UpStudy AI · Accepted Answer

**a)**  
First, we use the formula for the margin of error for a proportion at a $$ 95\% $$ confidence level:  
$$
\text{ME} = z\sqrt{\frac{p(1-p)}{n}},
$$  
where $$ z = 1.96 $$ for $$ 95\% $$ confidence, $$ p = 0.748 $$, and $$ n = 1997 $$.

1. Compute the standard error:
   $$
   \sqrt{\frac{0.748(0.252)}{1997}} = \sqrt{\frac{0.188496}{1997}} \approx \sqrt{0.000094468} \approx 0.009723.
   $$

2. Multiply by $$ z $$:
   $$
   \text{ME} = 1.96 \times 0.009723 \approx 0.019.
   $$

Rounded to three decimal places, the margin of error is $$ 0.019 $$.

---

**b)**  
The margin of error means that

$$
\text{One is } 95\% \text{ confident that the observed proportion of adults that responded "Wrong Track" is within } 0.019 \text{ of the population proportion}.
$$

Thus, choice D is correct.
a) The margin of error is 0.019. b) One is 95% confident that the observed proportion of adults that responded "Wrong Track" is within 0.019 of the population proportion.

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