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- I'll share everything to you. do you wanna go to the library?
- Hey Luna! I was absent yesterday, may I know what you did in our statistics class?
- Hey, yeah sure, actually we just had a discussion about "identifying the appropriate test statistics involving population mean in a real life problem".
- yeah sure.
- It is a t-test because the sample standard deviation is known and the standard deviation is less than 30.
- Yes that's correct. And also we can use Z-test if the population is known and the standard deviation is greater than 30, while in the central limit theorem, if the population is normally distributed or the sample size is large and the true population mean , then z has a standard normal distribution.
- Okay Eli here's an example. A manufacturer of tires claim that their tire has a mean life of at least 50.000 kms. A random sample of 28 of these tires is tested and the sample mean is 33.000 kms. Assume that the population standard deviation is 3.000kms and the lives if the first tires are approximately normally distributed. What kind of test is being used in this example?
- Can you please explain it to me how to identify the test statistics?
- Sure, we can just continue it there.
- okay... uhhm can you give me an example of it?
- Okay I'll give you an example and you'll be identifying what type of test statistic is being used but i am hungry can we go to the cafeteria first?
- Oh sure! to identify the test statistics, you must consider whether the population standard deviation/variance is known or unknown.
- If the population standard deviation/variance is known, then the mean has a normal distribution use Z-test. if the population standard deviation is unknown, then the mean has a t-test distribution, use t-test.
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