Question

Write a response addressing the following prompt: During presidential elections, election forecasters will typically use exit polls to try to predict the outcome of the presidential election. We will often hear that a candidate’s lead is “outside the margin of error” at a 95% confidence level. What does this mean? In your answer, be sure to include the following: Explain what margin of error and confidence intervals are. How does it help us estimate a population parameter? What does it mean when there is a “statistical tie”? Why is it dangerous to make predictions “within the margin of error”?

Answer 1

CONFIDENCE INTERVAL :- An estimator is a sample statistic used to estimate a population parameter .

example : x-bar can be a estimator of population mean .sample proportion can be a estimator of population proportion.

a point estimate is a single number that is used to estimate a unknown population parameter. A point estimate is always insufficient because it is either right or wrong.One needs to know how wrong it can be or its reliability.Therefore a point estimate is much more useful if it is accompanied by a estimate of error that might be involved.A interval estimate or confidence interval is a range of values used to estimate population parameter(with a known level of confidence or reliability)

MARGIN OF ERROR : - A margin of error tells you how percentage points your results will differ from the real population value .For example , a 95% confidence interval with a 4 percent margin of error means that your statistics will be within 4  percentage points of the real population value 95% of the time.More technically , the margin of error is the range of values below and above the sample statistics in a confidence interval.The confidence interval is a way to show what the uncertainty is with a certain statistics.

The terms 'statistical tie' is used to describe reported percentages that differ by less than a margin of error.

Dangerous to make predictions "within the margin of error" : -The idea behind confidence levels and margin of error is that any survey or poll will differ from the true population by a certain amount. However confidence interval and margin of error reflect the fact there is room of error , so although 95% confidence with 2% margin of error might sound like a very good statistic, room for error is bulit in , which means sometimes statistic are wrong. 95% of time your statistics will be within 2 percentage points of the real population value .It means if yours statistcs may not make inference about entire population.So, if you make predictions within margin of error ,there may be  huge difference between predicted and actual value.So your prediction might be better if you make predictions outside the margin of error at a certain confidene level.