Gallup regularly conducts polls asking U.S. adults if they approve of the job the president is doing. How did President Trump’s approval rating change from his first day in office to his 100th day in office?
According to a Gallup poll of 1500 randomly selected U.S. adults taken on his first day in office, 45% approved of Trump’s job performance.
Another Gallup poll of 1500 U.S. adults was taken on his 100th day in office and showed a 38% approval rating.
(a) Construct and interpret a 95% confidence interval for the change in the true proportions of U.S. adults who approved of Trump’s job performance from his first day to his 100th day in office.
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(b) Based on the confidence interval in part (a), what conclusion would you make about whether Trump’s approval rating has changed? Justify your answer.
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