statistics
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- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS KNOWN
- If the population standard deviation σ is known, then the mean has a normal distribution. Use z-test.
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- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS UNKNOWN
- What is a t-test?Like a z-test, a t-test also assumes normal distribution of the sample. A t-test is used when the population variance or standard deviationare not known.
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- 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).
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- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:CENTRAL LIMIT THEOREM
- 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.
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- 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.
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- T-testn 30, σ is not knownn ≥ 30, s is known
- 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 next time. Goodbye class!
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