How to determine the appropriate tool when the variance is known, variance is unknown, and when Central Limit Theorem is used?
To identify the test statistic (z or t-test), you must consider whether the population standard deviation is known/unknown.
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 .
TEST STATISTICSA test statistic is a random variable that is calculated from sample data and used in a hypothesis test.Z-TEST- is used to validate a hypothesis that the sample drawn belongs to the same population
SUMMARIZATION
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.
T-TEST- is used when the population variance or standard deviation are not known
Meanwhile like a z-test, a t-test also assumes a normal distribution of the sample.
When the variance is unknown and a sample size is less than 30 (n 30), use a t-test assuming that the population is normal or nearly normally distibuted.
CENTRAL LIMIT THEOREM (CLT)- if the population is normally distributed or the sample size is large and the true population mean u=u0, then z has a standard normal distribution.
When the variance is not known, we may still use the z-test/z-score by replacing the population standard deviation by the sample standard deviation 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 is known/unknown.
population standard deviation is known
n is greater that or equal to 30
z-test
population standard deviation is unknown
When the value of sample size (n)...
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
I will give examples for identifying the appropriate test statistic to be used in each problem, so listen carefully.