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- HOW TO DETERMINE APPROPRIATE TOOL WHEN:VARIANCE IS UNKNOWN
- On the other hand , when the Population Variance is Unknown, the appropriate test statistic to used is t-test.
- HOW TO DETERMINE APPROPRIATE TOOL WHEN:VARIANCE IS UNKNOWN
- What is a 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.
- 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 APPROPRIATE TOOL WHEN:VARIANCE IS UNKNOWN
- T-test
- Lastly, when the Central Limit Theorem (CLT) is used. the appropriate test statistics is using z-test by replacing population standard deviation (σ) by sample standard deviation (s) in the formula.
- HOW TO DETERMINE APPROPRIATE TOOL WHEN:CENTRAL LIMIT THEOREM
- 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 standard deviation (s) may be used as an estimate of the population standard deviation (σ) when the value of σ is unknown.
- The sample size is extremely large and the variance (σ2) is known or unknown.
- Z-test is the appropriate tool to used in central limit theorem when:
- HOW TO DETERMINE APPROPRIATE TOOL WHEN:CENTRAL LIMIT THEOREM
- REMEMBER:
- So, that is all for our lesson today. Thank you for listening. And, see you all on our next meeting. Goodbye class!
- n ≥ 30, σ is knownn ≥ 30, σ is unknown (Central Limit Theorem)n 30, σ is known
- Z-test
- n 30, σ is not knownn ≥ 30, s is known
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