The t-distribution is a continuous probability distribution that arises when estimating the mean of a normally distributed population in situations where:

• the sample size is small and
• the population standard deviation is unknown.

This application allows the user to interact with Student's t-distribution, modifying dynamically all the inputs. It plots the density distribution and show the desired confidence interval, comparing also with a Normal distribution if selected.

The link to the shiny app can be found here

The app assumes that the variable (x) has been previously normalized. The app needs the following inputs to work:

• Range of "x" values to be represented.
• Degrees of freedom: number of values that are free to vary (n-1).
• Confidence interval: desired level of confidence.
• Possibility to compare with a Normal distribution.

Once the desired inputs values have been selected, click on button "Apply and submit" to run the app.

Note that variables are set with default values.

The upper plot shows the t-Student's density distribution associated to the inputed values. If the Normal distribution compare checkbox is selected, the Normal density distribution is also plotted.

Below the plot, the t-confidence intervals (associated with the desired level of confidence) is shown.

Nothe that, if the Normal-comparasion checkbox is selected, the confidence intervals for the Normal distribution are also shown.

The following screenshot is an example of the app interface