Statistical Inference: Making conclusions about the population from sample data

In the first week of November of 2012, a national random telephone survey of 1101 adults was conducted by Gallup to see which presidential candidate they planned to vote for. The survey indicated that 46% planned to vote for Romney and 49% planned to vote for Obama, with a margin of error of +/- 3%. This result is an example of a confidence interval. A few days later, Americans voted for Obama with 51% of the vote, and Romney got 48% of the vote. Did this interval from the poll correctly predict the true proportion of voters for the two candidates? – Yes! Since the true value was within the margin of error, the poll correctly predicted the outcome! Obama’s prediction interval was 46-52%, and the true value was 51% Romney’s prediction interval was 43-49% and the true value was 48%

Estimating with Confidence: Confidence Intervals with Proportions In our large container, there are two types of beans, light and dark. What proportion of the beans are dark?

Confidence Intervals

Construct 80% and 95% confidence intervals for the proportion of dark beans based on your sample proportion.

Interpretations of intervals and levels Whenever you create a confidence interval, you should interpret it: – Interpret the confidence interval: use the level to estimate the true proportion of the population. For example, “We are 95% confident that between 46% and 52% of the population of Americans would vote for Obama.” This should not be confused with an interpretation of the confidence level: – Interpret the level of confidence: the level represents how likely we are to capture the true population parameter in repeated sampling. For example, for a 95% level, “95% of the intervals made for many samples will capture the true proportion.”