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 confidence intervals:

• A confidence interval for a population mean is an interval estimate of an unknown population parameter (the mean), based on a random sample from the population
  
  
• A confidence interval for a population mean is a set of plausible values of the parameter (m) that could have generated the observed data as a likely outcome.
  
  
• A confidence interval for a population mean consists of a sample statistic ( ) plus or minus a measure of sampling error (which is error from random sampling), when we have approximate normality of the sampling distribution.
  
  
• The level of confidence tells the probability the method produced an interval that includes the unknown parameter.
  
  
• The probability relates to the method (data, interval), not to the parameter.
  
  
• An increase in sample size leads to a decreased interval width: large samples have narrower widths than small samples (all other things being equal).
  
  
• Higher confidence levels have wider intervals than lower confidence levels (all other things being equal).
  
  
• Narrow widths and high confidence levels are desirable, but these two things affect each other.
  
  
• If many random samples are independently sampled from a population and 95% confidence intervals constructed for each one, we would expect about 5% intervals to not include the population mean (the population parameter). This 95% refers to the process of taking repeating samples and constructing confidence intervals for each.
  
  
• Confidence intervals for a population mean should be based upon a t statistic when the population distribution is approximately normal (or at least not too skewed) and s is unknown.
  
  
• A confidence interval suggests what parameter values are reasonable given the data and all values in the interval are equally plausible as values of m that could have produced the observed sample mean.
  
  
• After you calculate one confidence interval, the parameter is either included or not, but you don't know.
  
  
• It is desirable to have a narrow width (for more precise estimates) with a high level of confidence. A narrow width alone is not sufficient (if it has a low level of confidence).

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

• Know how to make a confidence interval wider or narrower (what factors can be changed)
  
  
• Know how to compute a confidence interval for a mean given sample data
  
  
• Know how to interpret a confidence interval, make an appropriate inference (in context) and be able to make a correct probability statement as an interpretation of a confidence

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III. Some common misconceptions students should NOT have:

• there is a 95% chance the confidence interval includes the sample mean
  
  
• there is a 95% chance the population mean will be between the two values (upper and lower limits)
  
  
• 95% of the data are included in the interval
  
  
• a wider interval means less confidence
  
  
• A narrower confidence interval is always better (regardless of confidence level)

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

• ideas of population, sample, parameter, statistics
  
  
• standard deviation of the sample mean, what it means (sigma divided by the square root of the sample size), how to find it, that it is a measure of variability of sample means, that it is based on a sampling distribution, what it tells about the variability of the sample mean
  
  
• sampling variability/sampling error, standard error (s divide by root n)
  
  
• mean, standard deviation
  
  
• the concept of probability
  
  
• z distribution
  
  
• estimates come from samples, the true value can only be obtained by knowing the population
  
  
• these estimates are close, but not exact, to the population parameter
  
  
• sampling distribution

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