Question

for a curve with ( d f = 39 ), find each ( t ) - value in parts (a) through (d) below, and illustrate the results graphically.
click the icon to view a partial ( t ) - table.
a. the ( t ) - value having area ( 0.05 ) to its right
( t = 1.685 )
(round to three decimal places as needed.)
choose the correct graph below.

b. ( t_{0.10} )
( t=square )
(round to three decimal places as needed.)

Explanation:

Step1: Recall the t - distribution table

We use the t - distribution table. The degrees of freedom \(df=n - 1\). Here \(n = 39\), so \(df=39 - 1=38\).
For \(t_{0.10}\), we are looking for the t - value such that the area to the right of it is \(0.10\).

Step2: Look up the value in the t - table

Looking at the row corresponding to \(df = 38\) (if the exact \(df\) is not available, we can use a close - by value or interpolation. In many standard t - tables, for large \(df\) (since \(38\) is relatively large and close to the normal approximation), and looking at the column for one - tailed area \(0.10\)).
The value of \(t\) with \(df = 38\) and one - tailed area \(0.10\) is \(t=1.304\)

Answer:

\(1.304\)