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- When the Population Variance is known, the appropriate test statistic to used is z-test. A z-score is calculated with population parameters such as “population mean” and “population standarddeviation”. It is used to validate a hypothesis that the sample drawn belongs to thesame population. When the variance is known and either the distribution is normalor sample size is large, use a z-test statistic.
- 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.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 (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 (n30).
- 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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