SITEMAP ABOUT
MiC Quality

SIX SIGMA GLOSSARY

  PROCESS IMPROVEMENT AND SIX SIGMA
ONLINE COURSES FREE TRIAL SIX SIGMA FAQ BROCHURES LICENSES ENROLL
GLOSSARY
:: Online Courses
:: Free Trial
:: Six Sigma
>> Glossary
>> Calculators
>> Reference Tables
>> Book Reviews
>> Black Belt ASQ
:: FAQ
:: Brochures
:: Licenses
:: Discounts
 
Welcome to MiC Quality Six Sigma Resources
Online Course Instructor
Glen Netherwood
MiC Quality
Online Learning
:: Home ::Six Sigma ::SIX SIGMA GLOSSARY: Sample Size with Hypothesis Tests :: CURRENT STUDENTS LOGIN

[SIX SIGMA GLOSSARY ALPHABETICAL INDEX] [SIX SIGMA GLOSSARY INDEX OF TOPICS]

Sample Size with Hypothesis Tests
 

Based on a level of significance 'α', and a Type II error 'β' at a departure 'δ' from the target mean, the formula for the t-test (small sample sizes) is:

where:

tα the t statistic corresponding to the chosen level of significance (use tα/2 for two sided tests)
tβ the t statistic corresponding to the Type II error (use for both one and two sided tests)

Note that:

The formula for the z test (large sample size) is essentially the same. For large sample sizes the t statistic converges to the z statistic:

where:

zα the z statistic corresponding to the chosen level of significance (use zα/2 for two sided tests)
zΒ the z statistic corresponding to the Type II error (use for both one and two sided tests)

Note that:

  • for two sided tests use α/2, but still use β (NOT β/2)
  • the standard deviation must be known to use either formula, although a reasonable estimate will serve
  • because the t-statistic depends on the number of degrees of freedom (n-1) the equation is solved iteratively. Start with the z-statistic and find an approximation for 'n' (or guess n). Use this value of 'n' to find the t statistic and recalculate to get a better approximation for 'n'. Repeat until the values converge.
 

Analytical and descriptive statistics are covered in the MiC Quality online course Primer in Statistics.

Try out our courses by taking the first module of the Primer in Statistics free of charge.

  Enroll Now
[SIX SIGMA GLOSSARY ALPHABETICAL INDEX] [SIX SIGMA GLOSSARY INDEX OF TOPICS] [Top]

MiC Quality Courses
:: Six Sigma Primer
:: Primer in Statistics
:: Advanced Statistics
:: Statistical Process Control SPC
:: Advanced SPC
:: Design of Experiments
:: Advanced DOE
:: Measurement Systems Analysis MSA/ Gage R&R
   
Primer in Statistics
FREE First Module
"Introduction to Statistics"

PDF

Primer in Statistics
FREE Reference Booklet

FREE Excel Primer
   
Learn More



 
Copyright 1998-2014 MiC Quality Legal Notices and Privacy Policy