Sampling Distributions and Confidence Intervals

• Update on CoursePack: Still in processing…
• Blogs will start NEXT week - stay tuned for blogging prompt
  • Homework Assignment #1 UPDATE (due Monday, September 5):
  • OpenStats, Chapter 4: 4.6.1 Variability in estimates (p. 203) - #4.3, 4.5
  • OpenStats, Chapter 4: 4.6.2 Confidence intervals (p. 206) - #4.8, 4.10, 4.14, 4.16
  • Depending on class today, exercises on Hypotheses Testing
• Reading assignment for Monday (posted on BB): OpenIntro Stats, Chapter 7: Introduction to Linear Regression

Definition: A parameter is a quantity describing a population, whereas an estimate or statistic is a related quantity calculated from a sample.

Parameter examples: Averages, proportions, measures of variation, and measures of relationship

Definition: The sampling distribution represents the distribution of the point estimates based on samples of a fixed size from a certain population. It is useful to think of a particular point estimate as being drawn from such a distribution. Understanding the concept of a sampling distribution is central to understanding statistical inference.

Definition: The standard deviation associated with an estimate is called the standard error. It describes the typical error or uncertainty associated with the estimate.

The standard error is also the standard deviation of the sampling distribution.

http://www.zoology.ubc.ca/~whitlock/kingfisher/SamplingNormal.htm

Definition: The standard error represents the standard deviation associated with the estimate, and roughly 95% of the time the estimate will be within 2 standard errors of the parameter.

An approximate 95% confidence interval for a point estimate is given by $$\textrm{point estimate} \pm 1.96\times SE$$

Note: For a yuge number of computed 95% confidence intervals, the population parameter will be contained in 95% of the confidence intervals.

http://www.zoology.ubc.ca/~whitlock/kingfisher/CIMean.htm