Please help with the following problems. Provide step by step calculations and diagrams.
a. What is the difference in appearance between a t-distribution and a z-distribution? Why do they have slightly different appearances?
b. When do we use a t-distribution rather than a z-distribution?
Please see the attached file for the complete solution with diagrams.
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a. t- distribution is a probability distribution that is often used when the population standard deviation is not known or when the sample size is small. t- distribution is symmetrical, bell-shaped, and similar to the standard normal curve. It differs from the standard z-distribution curve, however, in that it has an additional parameter, called degrees of freedom, which changes its shape.
Figure 1. t-distribution ...
The difference between a T-Distribution and Z-Distribution is discussed in this posting. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.