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- 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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