MA19.A2.32

Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.32

Produce a sampling distribution by repeatedly selecting samples of the same size from a given population or from a population simulated by bootstrapping (resampling with replacement from an observed sample). Do initial examples by hand, then use technology to generate a large number of samples.

Unpacked Content

Knowledge

Students know:
  • Techniques for producing a sampling distribution.
  • Properties of a normal distribution.

Skills

Students are able to:
  • Produce a sampling distribution.
  • Reach accurate conclusions regarding the population from the sampling distribution.
  • Accurately create and interpret a confidence interval based on observations from the sampling distribution.

Understanding

Students understand that:
  • The central limit theorem in statistics states that, given a sufficiently large sample size, the sampling distribution of the mean for a variable will approximate a normal distribution regardless of that variable's distribution in the population.
  • A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population. With large samples, you know that mean with much more precision than you do with a small sample, so the confidence interval is quite narrow when computed from a large sample.

Vocabulary

  • Bootstrapping
  • Population mean
  • Approximately normal
  • Standard deviation
  • Confidence interval

Aligned Learning Resources

ALSDE LOGO