Unknown Story

Hey, Lian. I'd like to ask you something. Can I?
Yeah, sure. Go ahead.
Let us say that the population variance is known, has normal distribution, 𝑛 ≥ 30, and the population standard deviation is known. What would be the appropriate test statistic shall I use?
Cool, thanks!
z-test
Hello, Zach. Would you mind if I ask you a question?
No, what is it?
I have a situation wherein the population variance is unknown, the population is normal or nearly normally distributed, 𝑛 30, the sample standard deviation is known, and the population standard deviation is unknown. What do you think is the appropriate test statistic shall I use?
Okay, thanks!
t-test
Hi, Macy. Do you think you could spare me a minute?
Of course. What would you like to talk about?
Well, let's say that the Central Limit Theorem is used, the population may not be normally distributed, 𝑛 ≥ 30 or considered sufficiently large, and the variance may be known or unknown. What do you think is the appropriate test statistic shall I use?
Great, thank you!
You should use z-test by replacing population standard deviation (𝜎) by sample standard deviation (𝑠) in the formula.

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