# Statistics : T-Distribution and Z-Distribution

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?

© BrainMass Inc. brainmass.com October 24, 2018, 6:23 pm ad1c9bdddfhttps://brainmass.com/statistics/students-t-test/statistics-t-distribution-z-distribution-39207

#### Solution Preview

Please see the attached file for the complete solution with diagrams.

Thanks for using BrainMass.

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 ...

#### Solution Summary

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.

Statistics T-distribution: A sample size approaches infinity; mayoral election is contested

1. As a sample size approaches infinity, how does the student's t distribution compare to the normal z distribution? When a researcher draws a sample from a normal distribution, what can one conclude about the sample distribution? Explain.

2. A mayoral election race is tightly contested. In a random sample of 1,100 likely voters, 572 said that they were planning to vote for the current mayor. Based on this sample, what is the initial hunch? Would one claim with 95% confidence that the mayor will win a majority of the votes? Explain.

View Full Posting Details