1. Because of the constantly evolving political climate around the United States, Gallup (uwho regularly conducts polls in the U.S.) conducted a poll just after the inauguration asking U.S. adults if they approve of the initiatives President Biden had implemented in his first few days in office. Another Gallup poll was conducted now that President Biden has been in office for a month asking U.S. adults if they approve of the initiatives President Biden had implemented after his first month in office. According to the first Gallup poll of 1500 randomly selected U.S. adults, 64% approved of the initiatives President Biden had implemented in his first few days in office. And according to the second Gallop poll of 1700 U.S. adults, 54% approved of the initiatives President Biden had implemented after his first month in office. A. Construct and interpret a 95% confidence interval for the change (difference) in the true proportion of U.S. adults who approved of the initiatives President Biden had implemented in his first few days in office to after his first month in office. B. Based on your interval, what conclusion would you make about whether President Biden's approval rating has changed. Justify your answer.

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1. Because of the constantly evolving political climate around the United
States, Gallup (who regularly conducts polls in the U.S.) conducted a poll
just after the inauguration asking U.S. adults if they approve of the
initiatives President Biden had implemented in his first few days in office.
Another Gallup poll was conducted now that President Biden has been in
office for a month asking U.S. adults if they approve of the initiatives
President Biden had implemented after his first month in office.
According to the first Gallup poll of 1500 randomly selected U.S. adults,
64% approved of the initiatives President Biden had implemented in his
first few days in office. And according to the second Gallop poll of 1700
U.S. adults, 54% approved of the initiatives President Biden had
implemented after his first month in office.
A. Construct and interpret a 95% confidence interval for the change
(difference) in the true proportion of U.S. adults who approved of the
initiatives President Biden had implemented in his first few days in
office to after his first month in office.
B. Based on your interval, what conclusion would you make about
whether President Biden's approval rating has changed. Justify your
answer.
5.700
Transcribed Image Text:1. Because of the constantly evolving political climate around the United States, Gallup (who regularly conducts polls in the U.S.) conducted a poll just after the inauguration asking U.S. adults if they approve of the initiatives President Biden had implemented in his first few days in office. Another Gallup poll was conducted now that President Biden has been in office for a month asking U.S. adults if they approve of the initiatives President Biden had implemented after his first month in office. According to the first Gallup poll of 1500 randomly selected U.S. adults, 64% approved of the initiatives President Biden had implemented in his first few days in office. And according to the second Gallop poll of 1700 U.S. adults, 54% approved of the initiatives President Biden had implemented after his first month in office. A. Construct and interpret a 95% confidence interval for the change (difference) in the true proportion of U.S. adults who approved of the initiatives President Biden had implemented in his first few days in office to after his first month in office. B. Based on your interval, what conclusion would you make about whether President Biden's approval rating has changed. Justify your answer. 5.700
Expert Solution
Step 1

Given;

n= 1500

P= 0.64

n= 1700

P= 0.54

Formula Used:

Confidence Interval for the difference between two proportions

CI = (P1 - P2± Zα/2P1(1-P1)n1+P2(1-P2)n2

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