STAT AND PROB
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- Making a comics strip on how to determine the appropriate tool when the variance is known, variance is unknown, and when Central Limit Theorem is used.
- SUBMITTED BY: DIANA C. ESGUERRASECTION:11-ICT RELIABLESUBMITTED TO:ELIZA DE VERA
- How to determine the appropriate tool when the variance is known?
- When Population Variance is Known?Let's start by acknowledging that it is completely unrealistic to think that we'd find ourselves in the situation of knowing the population variance, but not the population mean. Therefore, the hypothesis testing method that we learn on this page has limited practical use. We study it only because we'll use it later to learn about the power of a hypothesis test (by learning how to calculate Type II error rates). As usual,.
- Variance is unknown, and When Central Limit Theorem is used?
- Theorem (Central limit theorem)For large samples, the distribution of the sample mean is approximately Normal. If we have a random sample of size nn from a parent distribution with mean μμ and variance σ2σ2, then as nn grows large the distribution of the sample mean X¯X¯ tends to a Normal distribution with mean μμ and variance σ2nσ2n.The extremely useful implication of this result is that, for large samples, the distribution of the sample mean is approximately Normal.
- When Population Variance-is Unknown Now that, for purely pedagogical reasons, we have the unrealistic situation (of a known population variance) behind us, let's turn our attention to the realistic situation in which both the population mean and population variance are unknown.Note: For the central limit theorem to apply, we do need the parent distribution to have a mean and variance! There are some strange distributions for which either the variance, or the mean and the variance, do not exist. But we need not worry about such distributions here.
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