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- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS KNOWN, UNKNOWN, AND WHEN THE CENTRAL LIMIT THEOREM IS USED.
- Good morning, class! Our lesson for today is about how to determine the appropriate tool when the variance is known, the variance is unknown, and when the Central Limit Theorem is used. 
- When the Population Variance is Known, the appropriate test statistic to used is z-test.REMEMBER:z-test is the appropriate tool to used when:The population standard deviation (σ) is known.The sample standard deviation (s) is unknown.The population is normal normally distributed.The sample size is greater than or equal to 30.
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS KNOWN
- On the other hand, when the Population Variance is Unknown, the appropriate test statistic to used is t-test.REMEMBER:t-test is the appropriate tool to used when:The population standard deviation (σ) is unknown.The sample standard deviation (s) is known.The population is normal or nearly normally distributed.The sample size is less than 30 (n<30)
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS UNKNOWN
- Lastly, when the Central Limit Theorem (CLT) is used, the appropriate test statistic is using z-test by replacing population standard deviation (σ) 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:If the population is normally distributed or the sample size is large and the true population means μ = μo, the z has a standard normal distribution.The sample size is extremely large and the variance (σ2) is known or unknown.The sample standard deviation (s) may be used as an estimate of the population standard deviation (σ)  when the value of σ is unknown.
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:CENTRAL LIMIT THEOREM
- Z-testn ≥ 30,  σ is knownn ≥ 30,  σ is unknown (Central Limit Theorem)n < 30, 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,  σ is not knownn ≥ 30,  s is known 
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