A confidence interval for a mean gives a range of plausible values for the mean in the population or the theoretical world based on the data we’ve observed in the real world. In this video, we’ll consider how to calculate a confidence interval for a mean, and introduce a necessary probability distribution.
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Notes on the Video: Confidence Intervals for Means
Accessibility note: Plots at 6:10 and 6:36 in the video rely on colour to differentiate between two curves. See the notes for versions of the plots that use different line types to differentiate between the curves.
A point to consider for this video
The variability in the distribution of the individual observations is denoted by σ and is estimated by s, the standard deviation of the data values. The variability in x̅ is given by its standard deviation σ/√n, which is estimated by s/√n. s/√n is often called the standard error of the mean.
More on the t Distribution
This video introduced a new probability distribution, the t distribution. You can read more about it in these notes on the t distribution.
A t Distribution table can be used to find probabilities and quantiles for values from t distributions. This t table is from OpenIntro Statistics (external link, opens in new window) (licensed under the Creative Commons BY-SA 3.0 license).
In practice, statistical software is typically used to obtain probabilities and quantiles from t distributions. The Probability Distribution Calculator is an app that can be used for this.