- TEST STATISTICS
- A test statistic is a random variable that is calculated from sample data used in a hypothesis test.
- To identify the test statistic (z or t-test), you must consider whether the population standard deviation is known/unknown.
- Z-TEST 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 (n is greater that or equal to 30), use 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 (µ) and population standard deviation (σ).
- T-TEST is used when the population variance (σ^2) or standard deviation (σ) are not known
- When the variance is unknown and a sample size is less than 30 (n30), use a t-test assuming that the population is normal or nearly normally distributed.
- Meanwhile like a z-test, a t-test also assumes a normal distribution of the sample.
- CENTRAL LIMIT THEOREM (CLT) if the population is normally distributed or the sample size is large (n≥30) and the true population mean µ = µ0, then z has a standard normal distribution.
- When the variance is not known, we may still use the z-test by replacing the population standard deviation (σ^2) by the sample standard deviation (s) in the formula.
- For some cases, the CLT is used. In CLT, the population may not be normally distributed, sample is greater than or equal to 30 or sufficiently large, and variance (σ) is known/unknown.
- SUMMARIZATION
- population standard deviation is known
- Z-TEST
- n is greater thanor equal to 30
- When the value of sample size (n)...
- population standard deviation is unknown
- To have a better understanding of the lesson. Let's take a look at this...
- population standard deviation is known
- Z-TEST
- n is less than 30
- population standard deviation is unknown
- T-TEST
- Now, that is how you can identify the appropriate test statistics
- And that's the end of our lesson for today. See you all in our next class. Thank you and God bless.
- Thank you sir!

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