Question 8: Use the t-table (Table B in your book) to fill in this table.

The values you are looking up are denoted as t_{, df} where is the area in the upper tail of the t- distribution, and dfis the degrees of freedom.

a) Fill in the table below:

b) Are the values the t-table gives for infinite degrees of freedom the SAME answer you would have gotten had you looked up the appropriate z-value from the standard normal tables that had the same area of in the upper tail (yes/no)?

c) Is there a big difference between the critical value from the t-table based on 100 degrees of freedom and the standard normal critical value for the same area in the upper tail (yes/no)?

d) Assume we have 12 degrees of freedom, what is the area in the upper tail for a t-value of 2.179.?

Hint: look at the row with 12 degrees of freedom and find 2.179, and find the area in the upper tail

e) Assume we have 12 degrees of freedom, what is the area in the upper tail for a t-value of 2.681?

f) Assume we have 12 degrees of freedom, what two values must the area in the upper tail be between for a t value of 2.2? Hint: look at the row with 12 degrees of freedom and scan across that row until you find where 2.2 fallsit falls between 2.179 and 2.681 - so what does that mean the area in the upper tail for 2.2 is bounded between?

g)Assume we have 12 degrees of freedom, what two values must the area in the lower tail be between for a t value of -2.2 (Hint: remember the t-distribution is symmetric)

h) Assume we have 12 degrees of freedom, what two values must the area in the lowertail be between for a t value of 2.2 (Hint: remember the area under the whole curve is 1.0)

i) Assume we have 5 degrees of freedom and we have a t-value of 2.2 what two values must the area in the upper tail be between?

j)Assume we have 5 degrees of freedom and we have a t-value of -2.2, what two values must the area in the lower tail be between?