Question

a morning consult/politico poll of 1997 registered voters in july 2020 asked a standard polling question of whether the united states was headed in the
ight direction\ or was on the \wrong track.\ 75% said that things are on the wrong track vs. 25% who said
ight 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 99% confidence.
me = \square (round to three decimal places as needed.)

Explanation:

Step1: Identify key values

Sample size $n=1997$, sample proportion $\hat{p}=0.75$, confidence level 99%

Step2: Find z-critical value

For 99% confidence, $z^*=2.576$

Step3: Apply margin of error formula

$$ME = z^* \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$
Substitute values:
$$ME = 2.576 \times \sqrt{\frac{0.75(1-0.75)}{1997}}$$
$$ME = 2.576 \times \sqrt{\frac{0.75 \times 0.25}{1997}}$$
$$ME = 2.576 \times \sqrt{\frac{0.1875}{1997}}$$
$$ME = 2.576 \times \sqrt{0.000093891}$$
$$ME = 2.576 \times 0.00969$$

Step4: Calculate final value

$$ME \approx 0.025$$

Answer:

0.025