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  • HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS UNKNOWN
  • When the population variance is unknown, the t-test is the appropriate test statistic to use.
  • What is a t-test?A t-test is an inferential statistic that is used to see if there is a significant difference in the means of two groups that are related in some way.
  • HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS UNKNOWN
  • REMEMBER:T-test is the appropriate tool to used when:The standard deviation (σ) of the population is unknown.The sample standard deviation (s) is known.The population distribution is normal or nearly normal.The sample size is under 30 (n30).
  • HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS UNKNOWN
  • Finally, when applying the Central Limit Theorem (CLT), the appropriate test statistic is z-test, with population standard deviation () replaced by sample standard deviation (s) in 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:The z has a standard normal distribution if the population is normally distributed or the sample size is large and the true population means μ = μoThe sample size is enormous, and the variance (σ2) is either known or unknown.When the value of σ is unknown, the sample standard deviation (s) can be used to estimate the population standard deviation(σ).
  • HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:CENTRAL LIMIT THEOREM
  • That concludes our lesson for today. Thank you for your time. And I hope to see you all at our next meeting. Hello, class!
  • Z-testn ≥ 30, σ is knownn ≥ 30, σ is unknown (Central Limit Theorem)n 30, σ is known
  • T-testn 30, σ is not knownn ≥ 30, s is known
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