3. 2010 Healthcare Law. On June 28, 2012 the U.S. Supreme Court upheld the much

Question

3. 2010 Healthcare Law. On June 28, 2012 the U.S. Supreme Court upheld the much debated 2010 healthcare law, declaring it constitutional. A Gallup poll released the day after this decision indicates 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 statements are true or false, and explain your reasoning. (a) We are 95% confident that between 43% and 49% of Americans in this sample support the decision of the U.S. Supreme Court on the 2010 healthcare law. (b) We are 95% confident that between 43% and 49% of Americans support the decision of the U.S. Supreme Court on the 2010 healthcare law (c) If we considered many random samples of 1,012 Americans, and we calculated the sample proportions of those who support the decision of the U.S. Supreme Court, 95% of those sample proportions will be between 43% and 49%. (d) The margin of error at a 90% confidence level would be higher than 3%.

Explanation / Answer

95% Confidence interval means: based on our sample data, we are 95% confident that the "true" rate at Americans who support the decision is between (46-3)%=43% and (46+3)%=49%. Hence statement (a) is not correct whereas Statement (b) is correct. Since the confidence interval is defined for the true rate, not for sample rate hence Statement (c) is not correct. If the confidence level is decreased then the length of interval or margin of error is also decreased. Hence Statement (d) is false. Therefore,

(a) is false, (b) is true, (c) is false, (d) is false.

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