Statistics
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- What is a z-test?In a z-test, the sample is assumed to be normally distributed. A z-score is calculated with population parameters such as “population mean” and “population standard deviation”. It is used to validate a hypothesis that the sample drawn belongs to the same population. When the variance is known and either the distribution is normal or sample size is large, use a z-test statistic.
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS KNOWN
- The mean has a normal distribution if the population standard deviation σ is known. Also the appropriate test statistic to used is z-test.
- 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.
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS KNOWN
- REMEMBER:Population Variance Is Known when:Population is normally distributed.𝑛 ≥ 30Population standard deviation (𝜎) is known.z-test
- NOTE: Like a z-test, a t-test also assumes a normal distribution of the sample. A t-test is used when the population variance or standard deviation are not known. When the variance is unknown and a sample size is less than 30, use a t-test statistic assuming that the population is normal or approximately normal.
- HOW TO DETERMINE THE 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.
- REMEMBER:Population Variance Is Unknown when:Population is normal or nearly normally distributed.𝑛 30Sample standard deviation (s) is known. Population standard deviation (𝜎) is unknown.t-test
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS UNKNOWN
- REMEMBER:Central Limit Theorem test statistic is appropriate when:Population may not be normally distributed.𝑛 ≥ 30 or considered sufficiently largeVariance is known/unknown.Use 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
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