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

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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 Summary

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

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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 ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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