USA today provided a \"snapshot\" illustrating poll results from 21,944 subjects
ID: 3366030 • Letter: U
Question
USA today provided a "snapshot" illustrating poll results from 21,944 subjects. The illustration showed that 43% answered "yes" to this question : " Would you rather have a boring job than no job?" The margin of error was given as plus and minus 1 percentage point.
1. Describe what is meant by the statement that the "the margin of error is plus and minus 1 percentage point".
2. Also, we are given that 43% of 21,944 people polled answered "yes". Given that 43% is the best estimate of the population percentage, why would we need a confidence interval?
3. What additional information does a confidence interval provide.
Explanation / Answer
Solution: 1. Describe what is meant by the statement that the "the margin of error is plus and minus 1 percentage point".
The margin of error is the maximum expected difference between the true population parameter and a sample estimate of that parameter.
So here margin of error plus and minus 1 means the maximum difference between the true proportion and sample proportion that showed Yes to the given question = 1%. That means we would expect that between 42% (= 43% – 1%) and 44% (= 43% + 1%) of the population would answer "Yes" to the given mentioned question, based on the sample results.
2. Also, we are given that 43% of 21,944 people polled answered "yes". Given that 43% is the best estimate of the population percentage, why would we need a confidence interval?
The confidence level describes the uncertainty associated with a sampling method. We always compute confidence interval at certain confidence levels. For example A confidence interval with 95% confidence level means that we would expect 95% of the interval estimates to include the population parameter. So confidence interval gives us how confident we are about the estimate of parameter, which margin of error doesn't give. Thus confidence interval tells us how reliable the estimate is.
3. What additional information does a confidence interval provide.
The additional information that confidence interval provides is the Information about the accuracy of estimate.
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