AMorning Consult/Politico poll of 1997 registered voters in July 2020 asked a standard polling question of whether the United States was headed in the "Right Direction" or was on the Wrong Track" $75.3 \%$ said that things are on the wrong track vs. $247 \%$ 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 $95 \%$ confidence $M E=\square$ (Round to three decimal places as needed)
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Answer
Rounding to three decimal places, the margin of error for the proportion of all U.S. adults who think things are on the wrong track for 95% confidence is \(\boxed{0.019}\).
Step 1 ：Given that the sample size \(n = 1997\), the sample proportion \(p = 0.753\), and the z-score \(Z = 1.96\) for a 95% confidence interval.
Step 2 ：The margin of error for a proportion in a population is given by the formula: \(ME = Z \sqrt{ (p*(1-p)) / n }\).
Step 3 ：Substitute the given values into the formula: \(ME = 1.96 \sqrt{ (0.753*(1-0.753)) / 1997 }\).
Step 4 ：Solving the above expression gives \(ME = 0.018915289981722167\).
Step 5 ：Rounding to three decimal places, the margin of error for the proportion of all U.S. adults who think things are on the wrong track for 95% confidence is \(\boxed{0.019}\).
