II. EVALUATION

How to determine the appropriate tool when the variance is known, the variance is unknown, and when Central Limit Theorem is used.
A test statistic is a random variable that is calculated from sample data and used in a hypothesis test.
Z - test- The population standard deviation (σ) is known.- The population is normally distributed.- A z - score is calculated with population parameters.- It is used to validate a hypothesis that the sample drawn belongs to the same population.- The sample size is large (n ≥ 30)
t - test- A t - test is used when the population variance or standard deviation (σ) are not known.- The population is normal or nearly normally distributed.- The sample size is less than 30 (n 30)
Central Limit Theorem- In Central Limit Theorem, if the population is normally distributed or the sample size is large and the true population mean μ = μo, then z has a standard normal distribution.- When the sample size is extremely large and the variance is 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.
z - test - n ≥ 30, σ is known.- n ≥ 30, σ is not known (Central Limit Theorem)- n 30 , σ is known.
t - test- n 30, σ is not known.- n 30, s is known.

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