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- Slajd: 1
- VARIANCE IS UNKNOWN
- USE T-TEST
- n 30
- If the variance is unknown but the sample standard deviation is known, and the sample size is less than 30, we will use t-test, assuming that the population is normal or approximately normal.
- Very Good, Sha! You may take your seat. Lastly, Matt, I would like you to explain when is the Central Limit Theorem used.
- Slajd: 2
- Good morning class! In identifying test statistics, you must consider whether the population standard deviation or variance is known or unknown. Can anyone tell me what is the appropriate tool to use if the variance is known?
- CENTRAL LIMIT THEOREM
- USE Z-TEST
- n ≥ 30
- In Central Limit Theorem, if the population is normally distributed or the sample size is large and the true population mean μ = μo , then z has a standard normal distribution.
- Good job, Matt! Moreover, we may still use z-score by replacing the population standard deviation (σ) by the sample standard deviation (s). Since the sample is large, the resulting test statistic still has a distribution that is approximately standard normal.
- Slajd: 3
- The Z-test, T-test, and Central Limit Theorem (CLT) are key statistical concepts with different roles. Z-test is used for large samples (n≥30) when the population variance is known, relying on the Z-score and a normal distribution. In contrast, T-test is for smaller samples (n30) with unknown variance, using the T-score and the t-distribution to estimate means. The CLT is a principle explaining that as sample size increases, sample means follow a normal distribution, no matter the population’s shape. This makes Z-tests and T-tests possible by ensuring normality in sampling. In simple terms, Z-tests handle large samples with known variance, T-tests manage small samples with unknown variance, and CLT explains why both work.
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