Advice:
This is a topic where I find the use of an applet particularly helpful to emphasize the idea that when we talk about 95% confidence, we are talking about a long run probability.
I find that an analogy between a fish net and the confidence interval works well with most students. They readily understand that the larger the net, but more confident you are in catching the fish. Placing the net at your best guess of the location of the fish works well too. You're also not going to catch the fish every time you throw the net. Increasing sample size is like having a better fish finder so you have a better guess at where the fish is located. A discussion of alternative analogies quickly gets students thinking about concepts and relating them to personal experience.
Applets:
http://www.rossmanchance.com/applets/Confsim/Confsim.html
This applet lets you choose between simulating confidence intervals for proportions (Wald, Adjusted Wald, and Score) and means (Z with sigma, t, and Z with s). For means you can adjust the values of mu, sigma, n, C, and number of intervals. It keeps a running count of what percentage of intervals actually capture the true population mean.
Good problems:
- Assuming all other factors have been held constant, is a 90% or a 95% confidence interval wider? Explain.
- Given the endpoints of a confidence interval, what is the margin of error and what is the sample mean (or proportion)?
- True False A larger sample size produces a wider confidence interval for μ.
- True False A larger sample mean produces a wider confidence interval for μ.
- True False A larger standard deviation produces a wider confidence interval for μ.
- True False A larger confidence level produces a wider confidence interval for μ.
Data Sets:
- For proportions is easy to get examples from recent polls, such as the Gallup poll. They usually report the sample size and margin of error.
- I like using M&M colors for proportions, since you can get the intended actual proportion from the company.
- For means, the data set for human body temperatures is interesting for students since the 95% confidence interval does not include 98.6 degrees Fahrenheit.
- Minitab file can also be downloaded from (see Chapter 5 Rossman Chance Investigating Statistical Concepts, Applications and Methods: temp.mtw)
- Descriptive statistics (temperatures are in degrees Fahrenheit):
Group n sample mean sample sd Women 65 98.39 0.74 Men 65 98.10 0.70 Combined 130 98.25 0.73