From the course: Statistics Foundations 4: Advanced Topics
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T-distribution vs. z-distribution
From the course: Statistics Foundations 4: Advanced Topics
T-distribution vs. z-distribution
- Sometimes we come across a small, but interesting data set. Other times we run our own experiment or survey, but our number of available observations is limited. A single sample that is very small. This can present us with a few issues. For these types of small data sets, we almost certainly do not have access to the population's standard deviation, and the small sample size creates issues in estimating the population's standard deviation from the small sample. Also with small sample sizes, while the distribution may look symmetrical, it doesn't exactly look like the bell-shaped curve you're used to seeing, and thus the central limit theorem cannot be applied to its full effect, which leads us to the Z-score. Without normally distributed data, we can't use the Z-score, and thus trying to create confidence intervals with these types of formulas without a Z-score, you can't do it. So what can you do?…
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