A random sample of likely voters showed that 60 planned to v

A random sample of likely voters showed that 60% planned to vote for Candidate X, with a margin of error of 3 percentage points and with 95% confidence. a. Use a carefully worded sentence to report the 95% confidence interval for the percentage of voters who plan to vote for Candidate X. b. Is there evidence that Candidate X could lose? c. Suppose the survey was taken on the streets of a particular city and the candidate was running for president of the country that city is in. Explain how that would affect your conclusion. a. Which of the following statements best describes the confidence interval for the percentage of voters who plan to vote for Candidate X? A. I am 95% confident that the population percentage of voters supporting Candidate X is between 60% and 63%. B. I am 95% confident that the population percentage of voters supporting Candidate X is between 57% and 63%. C. I am 95% confident that the population percentage of voters supporting Candidate X is between 57% and 60%. D. I am 95% confident that the population percentage of voters not supporting Candidate X is between 57% and 63%. b. Is there evidence that Candidate X could lose? A. There is evidence that the candidate could lose. The reason there is evidence is because the margin of error is 3%. B. There is no evidence that the candidate could lose. The reason there is no evidence is because 60% of the sample voters planned to vote for Candidate X. C. There is evidence that the candidate could lose. The reason there is evidence is because the interval is entirely above 50%. 00. There is no evidence that the candidate could lose. The reason there is no evidence is because the interval is entirely above 50%. c. Which of the following is the best explanation on how the survey would affect your conclusion? A. A sample from this particular city would not be representative of the entire country and would be worthless in this context. B. A sample from this particular city would be representative of the entire country and would be helpful in this context. C. A sample from this particular city would be representative of the entire country and would be worthless in this context. D. A sample from this particular city would not be representative of the entire country and would be helpful in this context.

Solution

confidence interval = mean +/- margin of error

mean = 60%

margin of error = 3%

a)

confidence interval = 60% +/- 3% = (57%,60%)

so, the correct choice is B)

b)

No , since the least votes he can get at 95% confidence is 57% which assures him a win

so , the correct choice is D)

c)

although it doesnot cover the entire population it helps to predicate

so, the correct choice is D)