Confidence Intervals for Proportions and Means

Name: Confidence Intervals for Proportions and Means
Author: StemPy Lab

A news report says that 52% of people back a new park, plus or minus 3 points.

Where do the 3 points come from, and what do they promise?
Build an estimate with a margin of error, check when the formula for a proportion can be trusted, and plan the size of a survey.
Then run a hundred surveys by simulation and see what a 95% confidence level really means.

3 lessons, about 1 h 20 min3 simulations10 problems3 practice questionsPython in every lesson

Course outline (3 lessons)

Lesson 1about 25 min
An estimate with a margin of error
A sample share is our best single guess for the true share, but it is almost never exactly right. A margin of error says how far off it is likely to be. This lesson builds the margin from the standard error and the number $1.96$ , and turns a guess into an interval.
1 simulation1 practice question1 Python program3 problems
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Lesson 2about 25 min
The interval for a proportion
The 95% confidence interval for a proportion is $\hat p \pm 1.96\sqrt{\dfrac{\hat p(1 - \hat p)}{n}}$ . It can be trusted only when its conditions hold: a random sample, enough successes and failures, and a sample that is a small part of the population. The same formula, turned around, tells you how many people to ask.
1 simulation1 practice question1 Python program4 problems1 Python lab
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Lesson 3about 30 min
What 95% confident means
A 95% confidence level describes the method, not one interval: in the long run, about 95 of every 100 intervals made this way catch the true value. This lesson shows it with a hundred simulated surveys, lists the wrong readings, compares other levels, and meets the interval for a mean.
1 simulation1 practice question1 Python program3 problems1 Python lab1 question set1 note
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10 questions · 20 min

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