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- Hello class, today, we're going to talk about variance and when we use the Central Limit Theorem.
- You can determine the appropriate test statistic by considering data type, number of groups, data distribution, relationship between samples, level of measurement, and number of samples, while adhering to test assumptions.
- HOW TO DETERMINE THE APPROPRIATE TOOL STATISTIC TO USE
- The appropriate statistical tool for determining the population mean is determined by conducting a Z-test or constructing a confidence interval using the known population standard deviation.
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN THE VARIANCE IS KNOWN
- When the variance is unknown, choose the T-distribution for confidence intervals if dealing with a small sample size, utilizing the sample standard deviation, and consider the normal distribution approximation for larger sample sizes following the Central Limit Theorem.
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN THE VARIANCE IS UNKNOWN
- The Central Limit Theorem's appropriate tool depends on the sample size. For larger samples (n 30), the Z-distribution is suitable for estimating population parameters, while for smaller ones, the T-distribution is preferred to account for potential variability from a limited sample.
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN CENTRAL LIMIT THEOREM IS USED
- That concludes our lesson for today. I appreciate you listening. I hope to see you all at our upcoming meeting. Farewell, class!
- Z-testn ≥ 30, σ is knownn ≥ 30, σ is unknown (Central Limit Theorem)n 30, σ is known
- T-testn 30, σ is not knownn ≥ 30, s is known
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