Question: A federal law that lowered the limit for a legal blood alcohol level for automobile drivers was signed by President Clinton in October 2000. At its website, the Gallup Organization reported the following survey results in an article dated October 26, 2000:
72% of Americans support lowering the drunk driving limit to 0.08% BAC A total 1,002 telephone interviews were conducted between July 20-Aug 3, 2000, with a representative sample of the U.S. public age 16 and older. The findings are based on 930 respondents who identified themselves as licensed drivers. The margin of error equals plus or minus three percentage points.
a. The first sentence of the information from the Gallup Organization states, "72% of Americans support lowering the drunk driving limit to 0.08% BAC." Considering the difference between a sample and a population, explain why this sentence is not necessarily correct. Rewrite the sentence so that it is correct.
b. The article provides the information that "the margin of error equals plus or minus three percentage points." Write one or two sentences interpreting this value that could be understood by someone who does not know anything about statistics.
c. Using the margin of error provided by the Gallup Organization, calculate a 95% confidence interval for the proportion that supported the lower legal blood alcohol limit at that time. Write a sentence that interprets this interval. Be sure to specify the appropriate population.
d. On the basis of the interval computed in part (c), is it reasonable to conclude that more than half of American licensed drivers supported the lower blood alcohol limit at that time?