1. What students should understand about this topic:
   
   
2. What students should be able to DO with this knowledge:
   
   
3. Some common misconceptions students should NOT have:
   
   
4. Prerequisite knowledge students should have before using the tools:
   
   
5. Simulation Software (Sampling SIM program)
   
   
6. Pretest: mostly of prerequisite knowledge, to give before using the tool as a diagnostic measure.
   
   
7. Activity that uses the software.
   
   
8. Posttest: including some pretest items, some items directly related to the software, and some application problems.
   

I. What students should understand about this topic:

• That a sampling distribution for means (based on quantitative data) is a distribution of sample means (statistics) of a given sample size, randomly sampled from a population with mean m and standard deviation s. It is a probability distribution for the sample mean.
  
  
• The sampling distribution for means has the same mean as the population (parameter)
  
  
• As n gets larger, variability of the sample means gets smaller (a statement, a visual recognition, and predicting what will happen or how the next picture will differ)
  
  
• Standard error of the mean is a measure of variability of sample statistic values
  
  
• Interpret area/apply areas under curve as probability statements about sample statistics
  
  
• The building block of a sampling distribution is a sample statistic
  
  
• Some values of statistics are more or less likely than others to be drawn from a particular population
  
  
• When it is reasonable to use a normal approximation
  
  
• Different sample sizes lead to different probabilities for the same value (know how sample size affects the probability of different outcomes for a statistic)
  
  
• Sampling distributions tend to look more normal than like the population, even for small samples
  
  
• As sample sizes get very large, all sampling distributions for means look alike (i.e., have the same shape), regardless of the population from which they are drawn
  
  
• Averages are more normal and less variable than individual observations
  
  
• Distinguish between a distribution of observations in one sample and a distribution of statistics (sample means) from many samples (n greater than 1) that have been randomly selected.

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II. What students should be able to DO with this knowledge:

• Describe what a sampling distribution would look like for different populations and sample sizes (in terms of shape, center and spread, and where the majority of values would be found). What values of the sample mean are likely, and which are less likely.
  
  
• Describe the size of the standard error of the mean
  
  
• Describe the likelihood of different values of the sample mean
  
  
• Describe the mean of the sample means for different shaped populations

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III. Some common misconceptions students should NOT have:

• Sampling distribution should look like the population (for n > 1)
  
  
• Sampling distributions for small and large sample sizes have the same variability
  
  
• Sampling distributions for large samples have more variability
  
  
• Don't understand that a sampling distribution is a distribution of sample statistics
  
  
• Confuse one sample (real data) with all possible samples (in distribution) or potential samples
  
  
• Representing a population (better for large samples) is confused with a sampling distribution for large samples, better representing a population (have more area)
  
  
• Students pay attention to the wrong things: e.g., heights of bars
  
  
• The mean of a positive skewed distribution will be greater than the mean of the sampling distribution for samples taken from this population

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IV. Prerequisite knowledge students should have before using the tools:

• The idea of a distribution
  
  
• What variability means (spread vs. smoothness)
  
  
• The idea of the center of a distribution
  
  
• A random sample
  
  
• A sample statistic vs. a population parameter
  
  
• Common shapes of distributions: normal, skewed, uniform, bimodal
  
  
• Being able to see between the data, to recognize overall shapes of distributions
  
  
• The idea of area under a curve and how it represents likelihood of outcomes
  
  
• Properties of the normal distribution
  
  
• Normal distributions can look different due to different variability (shape vs. variance)
  
  
• How to read and interpret histograms
  
  
• The idea of sampling variability

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