Sampling Distributions

Advice

• Do some hands-on sampling by having students select samples both randomly and by them choosing a representative sample.
• Let students build distributions from their samples and then discuss distributions.
  
• Hands on sampling should be done numerous times with different types of sampling in different contexts. (see below for three activities.)
• The website Tools for Teaching and Assessing Statistical Inference includes a list of This website has many activities, assessment questions, and very helpful lists of student misconceptions to guide you.

Applets

• Animated sampling distribution (for means)  Number of samples, number of samples, parent population can be chosen.  Sample statistic can be chosen from mean, standard deviation, biased and unbiased variance of sample, MAD, range
• Animated Reese's pieces Samples (for proportions) Sample size, number of samples, and population proportion (of orange Reese's pieces) can be chosen.
  
• The applet keeps track of the sample proportions of orange Reese's pieces drawn from a candy machine (animated) and creates a dotplot of the results of all the simulations, plots a normal curve, and computes the mean and standard deviation of all of the p-hat values of the simulations.
  
• This applet is particularly useful if you skipped teaching the binomial distribution. You can empirically verify the formulas for the mean and sd of p-hat using the applet output and visually see the shape of the normal distribution.
• It also lets you change values of n and p to see how the sampling distribution can become skewed when np<5 or nq<5.
  

 
Activity

• Cents and the Central Limit Theorem from Activity-Based Statistics by R.L. Scheaffer, A. Watkins, J. Witmer, M. Gnanadesikan, Key College Press  I can't count on my students having any change with them.  I start collecting pennies early in the semester bringing in nickels and dimes to trade with students.  The semester I collect, I find myself paying cash for more items.  I can use the pennies collected in one semester for two years before the students start to think the activity is "yellowed notes."  The tollbooth on the way to the airport takes pennies and I dispose of the coins that way.
• Sampling Rectangles from Activity-Based Statistics by R.L. Scheaffer, A. Watkins, J. Witmer, M. Gnanadesikan, Key College Press.
• Chapter 3 D. S. Moore Statistics: Concepts and Controveries has a page with 100 circles labeled 00 through 99 40% colored, 60% white.  Samples for proportions can be demonstrated.