Question

1. Explain the Frequentist interpretation of the confidence level. (Do NOT explain the Bayesian interpretation)

1. Consider presidential polls and the following headline: Polls show Hillary ahead at 51% (+/-3%), Trump lagging behind at 49% (+/-3%)
   • What is the confidence interval for each candidate?
   • Which candidate is really ahead?
   • Why is it important for the general public to understand confidence intervals?

Answer 1

A confidence interval with say 99% confidence tells us the range of values with 99% confidence that it contains the true value of the population parameter (the true proportion or mean) which we estimate from our sample dataset.

+-3% means we have a 99% confidence interval (since +- 3 from a standard normal curve is for 99%)

Hilary's range of values are therefore: (48%, 54%)

Trump's range of values are (46%, 52%)

Although their intervals overlap but there are chances of Hilary's polls having greater than 52% (highest of trump) and Trump's polls lower than 48% (lowest of Hilary) with 99% confidence. So Hilary is really ahead

But we can only say this with 99% confidence and not 100% surity hence it's important to understand confidence intervals to find proper range for estimates within which the Actual values can lie.