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  • HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS UNKNOWN
  • On the other hand, when the Population Variance  is Unknown, the appropriate test statistic to used is t-test.
  • What is a t-test?A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related in certain features.
  • HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS UNKNOWN
  • REMEMBER:T-test is the appropriate tool to used when:The population standard deviation&#160;(σ) is unknown.The sample standard deviation (s) is known.The population is normal or&#160;nearly normally&#160;distributed.The sample size is less than 30 (n<30).
  • HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS UNKNOWN
  • Lastly,&#160;when the Central Limit Theorem (CLT) is used, the appropriate test statistic is&#160;using z-test by replacing&#160;population standard&#160;deviation (σ) by sample&#160;standard deviation (s) in&#160;the formula.
  • HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:CENTRAL LIMIT THEOREM
  • REMEMBER:Z-test is the appropriate tool to used in central limit theorem when:If the population is normally distributed or the sample size is large and the true population means μ =&#160;μo, the z has a standard normal distribution.The sample size is extremely large and the variance (σ2)&#160;is known or unknown.The sample standard deviation (s) may be used as an estimate of the population standard deviation&#160;(σ)&#160;&#160;when the value of&#160;σ&#160;is unknown.
  • HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:CENTRAL LIMIT THEOREM
  • Z-testn ≥ 30,&#160;&#160;σ is knownn ≥ 30,&#160;&#160;σ is unknown (Central Limit Theorem)n < 30,&#160;σ is known
  • So, that is all for our lesson today. Thank you for listening. And, see you all on our next meeting. Goodbye class!
  • T-testn < 30,&#160;&#160;σ is not knownn ≥ 30,&#160;&#160;s is known&#160;
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