Today we introduced confidence intervals for population proportions. The 95% confidence interval is:
\[\hat{p} \pm 2 \sqrt{\frac{\hat{p}(1-\hat{p})}{N}}\] where \(\hat{p}\) is the sample proportion and \(N\) is the sample size. We did three examples:
11 out of 24 students in this class were born in VA. Find the 95% confidence interval for the percent of all HSC students who were born in VA.
If a psychic is able to correctly guess the correct image out of five choices 36% of the time on 25 tries, what is the confidence interval for the true portion they are able to get right using their psychic powers? Is this strong evidence that they have real powers, or could they just be lucky to be getting more than 20% right?
In political poll for an election with two candidates and a sample proportion of approximately 50%, how big of a sample would you need to get a margin of error that is less than 3%? Recall that the margin of error is the part of a confidence interval formula after the \(\pm\) sign.
Today we talked about how you can use confidence intervals to estimate the difference between two population means or proportions. We did this workshop in class: