Give an example of a confidence interval for a proportion with a margin of error of 5% that falls below zero for some of its values.
Answer: any answer that contains negative numbers as part of the interval and has width of 10%, such as 2% plus or minus 5%, which would be -3% to 7%. Name two different situations that can result in a confidence interval for a proportion falling into negative numbers for some of its values (which does not make sense). Give an example of each.
Answer: 1) a large margin of error caused by a small sample size (for example, 10% plus or minus 20%); or 2) a small sample proportion and a margin of error that’s larger than the sample proportion (for example, 2% plus or minus 5%). Which would be wider, a 90% confidence interval or a 95% confidence interval? (Assume both of them were calculated using the same sample data.) Explain your answer.
Answer: the 95% confidence interval is wider. Since the data sample size is the same and you want more confidence of covering the true population value, you need a larger margin of error, which results in a wider confidence interval. Suppose a survey was conducted to find out what proportion of Americans intend to vote in the next Presidential election. For which of the following confidence intervals would it be fair to conclude, with high confidence, that a majority of Americans will vote in the next Presidential election?
52% plus or minus 3%