Probability and Statistics

1. In the 2012 Presidential election, Florida was one of the swing states in which no single candidate or party had overwhelming support. In a poll completed November 1, just one week before the election, the Tampa Bay Times found 51% in favor of Romney, 45% in favor of Obama and 4% undecided. On November 3rd, the opening line in the article of the Tampa Bay Times that reported the results of this poll sais “Florida continues to look good for Mitt Romney.” The poll was based on a sample of 800 likely voters. On election day, Romney received 49.1% of the votes in Florida and lost the state. What happened?
a) For each of the boldface numbers, indicate whether it is a parameter or a statistic. Explain your answer.
b) Suppose 49.1% of all voters supported Mitt Romney at the time of the poll. What are the mean and the standard deviation of p^ (pHat), the proportion of voters in a SRS of 800 voters who would support Romney?
c) Suppose 49.1% of all voters supported Mitt Romney at the time of the poll. What is the probability that at least 51% of the voters in an SRS of 800 voters would support Romney?

2. Greeks bucked a global trend in which people in most countries except their lives in five years to be better than their current lives. Even among those countries with much lower current life ratings, greater than optimism was found because people cannot fathom their lives getting worse. But in Greece, only 25% expect their lives to be better in 5 years than currently. In an SRS of 500 greek citizens, what is the probability that less than 30% of the sample expect their lives in 5 years to be better than their current lives?

3. Approximately 20% of cars in the US are white. You take an SRS of 300 cars parked in student lots on your campus and find 42 are white. For this problem, you can assume that you have obtained an SRS of student cars on campus.
a) what is the proportion, p^, of white cars in your sample?
b) If 20% of student cars on campus are white, what proportion of samples wpuld give a value of p^ as small as the value computed in (a)?
c) There are two explanations for your sample result. The first is that you obtained a sample with an unusually low percentage of white cars. What is an alternative explanation?

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