# Statistics : T-Distribution, Z-Distribution and p-Values

Click on the link for Table 1 (Standard normal distribution-Z). You will see the z -distributions and t-distributions. I would like you to see the difference in the two. Say we have a test statistic of 1.50. We can plug in our numbers to compare how a z-distribution will look compared to a t-distribution. For Tables 1 click on two-tail, and then type in 1.50 for your z-value. For the t-distribution, you will also click on two-tail, and type in your 1.50 value. With this distribution, though, you need to also type in a df value. Let's use df = 29. Click on the arrows to the right to find the probability for each distribution,

a. What are these two p-values?

b. Are these p-values statistically significant?

c. What are the p-values indicating?

Now plug in the value 3.50 for both the z-distribution and the t-distribution (leave the df at 29 for the t-test).

d. What are your corresponding p-values now?

e. Are these p-values statistically significant?

Now plug in a value of your choosing for the test statistic (use the same df = 29). Use the same value for both distributions.

f. Tell me what value you used and the corresponding p-values.

g. Are the p-values statistically significant?

Please see attached for full question.

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#### Solution Preview

Please see the attached file for the complete solution.

There are applets with t and z-distributions at the following link: http://math.uc.edu/~brycw/classes/148/tables.htm

Click on the link for Table 1 (Standard normal distribution-Z). You will see the z -distributions and t-distributions. I would like you to see the difference in the two. Say we have a test statistic of 1.50. We can plug in our numbers to compare how a z-distribution will look compared to a t-distribution. For Tables 1 click on ...

#### Solution Summary

T-Distribution, Z-Distribution and p-Values are investigated. The solution is detailed and well presented.