Question

6. Use Minitab to construct graphs of pdfs of N(0, 1), f(t, 1), f(t, 5), f(t, 10) and f(t, 30) on the same graph. What relation between the standard normal distribution and the t distributions can be shown on the graph? *Submit the Minitab file saved with extension .MPJ for full credit not the snip of screen. (15)

Answer 1

As only 2 distributions can be plotted on the same graph, the 4 graphs are entered as follows:

[STEPS: At first, go the Graphs option, click on Probability Distributions plot. Choose the option with two distribution. Enter the parameters as required. Click on OK.]

Distribution Plot Distribution Mean StDev Normal 0 1 Distribution df T 1 Density - - 0.0 - - - - - -10 5 10 Ox

Distribution Plot Distribution Mean StDev Normal 0 1 Distribution df T5 Density 0.0 - -5 - -4 -3 -2 -1 0 1 2 3 4

Distribution Plot Distribution Mean StDev Normal 0 1 Distribution df T 10 Density 0. 02 -4 -3 -2 -1 0 1 3 4

Distribution Plot Distribution Mean StDev Normal 0 1 Distribution df 30 T Density 0.0 - -4 -3 -2 -1 0 1 2 3

As it is evident from the graphs, the distribution curve of the standard normal distribution and the t-distribution co-incide as the df increases from 1 to 30. In the first graph, there is considerable difference between the probability distribution curves of both the distributions. In the second graph, the difference is lowered. In the third graph, the difference decrease even more. Finally, in the 4th graph, the two curves coincide.

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