The z and t Statistic

One of the most basic hypothesis tests is a test about a population mean. A researcher might be interested in testing to determine whether an established or accepted mean value for an industry is still true or in testing a hypothesized mean value for a new theory or product.

 

The following z-test formula can be used to test hypotheses about a single population mean when σ is known and sample size n ≥ 30 and x is known to be normally distributed.

 

 

If n < 30 or x is not normally distributed:

 

If making a claim against one population proportion (p), if n < 30 and x is normally distributed:

 

 

 

 

If n < 30 or x is not normally distributed:

 

 

 

Hypotheses Testing for two means.

If n1 > 30, n2 > 30 and x is normally distributed:

H0: µ1 = µ2

Ha: µ1 ≠ µ2

 

 

 

 

If n1 < 30, n2 < 30 and x is not normally distributed:

 

 

 

 

Hypotheses testing for two proportions (p1, p2)

If n1 > 30, n2 > 30 and x is normally distributed:

 

 

 

 

If n1 < 30, n2 < 30 and x is not normally distributed:

 

 

Suggested Readings

  1. Statistics Glossary
    http://www.stats.gla.ac.uk/steps/glossary/hypothesis_testing.html
  2. Elon University Statistics Page
    http://math.elon.edu/statistics112/index.html
  3. Online Stats Book
    http://onlinestatbook.com/
  4. Statistics Explained
    http://www.animatedsoftware.com/ascodesc/statdesc.htm
  5. Data, Probability and Statistics
    http://www.mathsisfun.com/probability/index.html