For a t distribution with 16 degrees of freedom, find the area, or probability, in each region.
c. To the left of -1.746. (Use 2 decimals.)
d. To the right of 2.583. (Use 2 decimals.)
e. Between -2.120 and 2.120. (Use 2 decimals.)
f. Between -1.746 and 1.746. (Use 2 decimals.)
To find the area or probability in each region for a t-distribution with 16 degrees of freedom, we can use a t-table or a statistical calculator. Here's how you can find the answers using a t-table:
c. To the left of -1.746:
Step 1: Look for the closest value to -1.746 in the t-table. In this case, the closest value is -1.753.
Step 2: Find the corresponding probability in the table for 16 degrees of freedom. The value is 0.047.
So, the area to the left of -1.746 is approximately 0.05.
d. To the right of 2.583:
Step 1: Look for the closest value to 2.583 in the t-table. In this case, the closest value is 2.567.
Step 2: Find the corresponding probability in the table for 16 degrees of freedom. The value is 0.025.
So, the area to the right of 2.583 is approximately 0.03.
e. Between -2.120 and 2.120:
Step 1: Find the area to the left of 2.120 using the steps mentioned above. Let's say it is approximately 0.975.
Step 2: Find the area to the left of -2.120 using the steps mentioned above. Let's say it is approximately 0.025.
Step 3: Subtract the area to the left of -2.120 from the area to the left of 2.120.
0.975 - 0.025 = 0.95
So, the area between -2.120 and 2.120 is approximately 0.95.
f. Between -1.746 and 1.746:
Step 1: Find the area to the left of 1.746 using the steps mentioned above. Let's say it is approximately 0.95.
Step 2: Find the area to the left of -1.746 using the steps mentioned above. Let's say it is approximately 0.05.
Step 3: Subtract the area to the left of -1.746 from the area to the left of 1.746.
0.95 - 0.05 = 0.90
So, the area between -1.746 and 1.746 is approximately 0.90.