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Mathematics LibreTexts

6: Estimating Averages

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  • 6.1: The Central Limit Theorem for Sums
    The central limit theorem tells us that for a population with any distribution, the distribution of the sums for the sample means approaches a normal distribution as the sample size increases. In other words, if the sample size is large enough, the distribution of the sums can be approximated by a normal distribution even if the original population is not normally distributed.
  • 6.2: A Single Population Mean using the Student t-Distribution
    We rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation ss as an estimate for σσ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
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6: Estimating Averages is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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