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- A z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large.
- The appropriate tool when the variance is known
- The appropriate tool when the variance is unknown
- On the other hand, when the Population Variance is Unknown, the appropriate test statistic to used is t-test.
- The appropriate tool when the 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 (n<30).
- 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.
- The appropriate tool when the Central Limit Theorem is used
- 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.
- The appropriate tool when the Central Limit Theorem is used
- 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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