In 2012, the Supreme Court upheld the constitutionality of the Affordable Care Act (ACA), known colloquially as Obamacare. A Gallup poll conducted the day after this decision found that 46% of 1,012 Americans agree with this decision. At a 95% confidence level, this sample has a 3% margin of error. Based on this information, determine if the following four statements are true or false. Explain your reasoning. True or False and why? We are 95% confident that between 43% and 49% of the 1,012 sampled Americans support the decision. True or False and why? We are 95% confident that between 43% and 49% of all Americans support the decision. True or False and why? If we considered many different random samples of 1,012 Americans and, for each one, we calculated the sample proportions of those who support the decision, then 95% of those sample proportions will be between 43% and 49%. True or False and why? The margin of error at a 90% confidence level would be higher than 3%.
In 2012, the Supreme Court upheld the constitutionality of the Affordable Care Act (ACA), known colloquially as Obamacare. A Gallup poll conducted the day after this decision found that 46% of 1,012 Americans agree with this decision. At a 95% confidence level, this sample has a 3% margin of error. Based on this information, determine if the following four statements are true or false. Explain your reasoning.
True or False and why? We are 95% confident that between 43% and 49% of the 1,012 sampled Americans support the decision.
True or False and why? We are 95% confident that between 43% and 49% of all Americans support the decision.
True or False and why? If we considered many different random samples of 1,012 Americans and, for each one, we calculated the sample proportions of those who support the decision, then 95% of those sample proportions will be between 43% and 49%.
True or False and why? The margin of error at a 90% confidence level would be higher than 3%.
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