Overview
On this page, we discuss how to adjust our inference methods when estimating a proportion instead of a mean in a population.
Basic learning objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Understand that we can apply our results from last time to find a confidence interval for a population proportion by considering sampling from a Bernoulli distribution (where the parameter \(p\) is the mean).
Advanced learning objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Be able to construct confidence intervals for a population proportion at any confidence level when the population standard deviation is known, or approximate the interval when it isn’t known by using the fact that the margin of error is bounded: Since \(0\leq \sqrt{p(1-p)}\leq \frac{1}{2}\), we have \(E\leq z^{\ast}\, \frac{1}{2\sqrt{n}}\).
To prepare for class
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Watch the first half (up until 4:52) of the following video (by jbstatistics) which introduces the concepts of inference for a proportion (the second half of the video discusses Hypothesis Testing, which we will discuss later):
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Watch the first half (up until 3:36) of the following video (by jbstatistics) which goes through a detailed example of constructing a confidence interval for a proportion:
After class
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Watch the following video (by jbstatistics) which discusses more details about the sampling distribution of a a proportion:
