Central Limit Theorem

Hello Selena! Yes, Sure
Hello John! Can I ask you a question?
Yes, I remember the appropriate tool when the Variance is Known is z-test, To determine whether two population means are different when the variances are known and the sample size is large.
Do you remember on how to determine the appropriate tool when the Variance is Known is used?
I remember when the Variance is Unknown, the appropriate test statistic to used is t-test.
How about when the Variance is Unknown is used what is appropriate tool?
Selena, I also have a question Do you remember what our teacher says about how to determine the appropriate tool when CENTRAL LIMIT THEOREM is used?
Yes, I remember she saysWhen applying the Central Limit Theorem (CLT), the appropriate test statistic is z-testby replacing population standard deviation (σ) by sample standard deviation (s) in the formula.
Oh thank you! Also do you remember when the Z-test is the best tool to use in the CENTRAL LIMIT THEOREM?
Yes, It is used when:-The z has a standard normal distribution if the population is normally distributed or the sample size is large, and the true population meansμ = μo-The sample size is extremely large and the variance (σ2) is known or unknown.-When the value of is unknown, the sample standard deviation (s) can be used to approximate the population standard deviation (σ).
Thank you so much, Selena, for your help!
You're welcome and thank you also, John! It's nothing!

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