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== 12.2#h(0.6em)t Distribution Demo


    This section is an interactive demonstration. The live simulation runs on the original site: #link("https://onlinestatbook.com/2/tests_of_means/t_distribution_demo.html")[open the demonstration at onlinestatbook.com].


    Learning Objectives


    + State the difference between the shape of the t distribution and the shape of the normal distribution.
+ State how the degrees of freedom affect the difference between the t and normal distributions.


    #strong[Instructions] #linebreak() 
      
This demonstration allows you to compare the t distribution to the standard normal distribution. At the start, the standard normal distribution is compared to a t distribution with three degrees of freedom. You can change the degrees of freedom of the t distribution with the slider. The 3 and the 50 mark the ends of the slider. The "current" degrees of freedom are shown at the bottom where it says "t distribution with df=3." As you change the slider, the df are shown by this last line. The "zoom in" button allows you to change the scale of the graph to see the tails of the distribution in more detail.


    #strong[Illustrated Instructions] #linebreak() 
       Video Demo #linebreak() 
       
      In the video the slider is used to increase the degrees of freedom. Notice how the t-distribution change as the degrees of freedom increase. The video concludes with the tails of the tails of the graphs being zoomed into via the "zoom in" button and the degrees of freedom being decreased.


    #strong[Video Demo]


    You can change the shape of the t-distribution by adjusting the degrees of freedom with the sliders.


    #link("https://onlinestatbook.com/movies/tests_of_means/t_distribution_demo.mp4")[Watch the video demonstration (onlinestatbook.com)]