Question 3 of 13, Step 2 of 2 Consider the value of \( t \) such that the area to the left of \( -|t| \) plus the area to the right of \( |t| \) equals 0.1 Step 2 of 2 : Assuming the degrees of freedom equals 20 , select the \( t \)-value from the \( t \)-distribution table.

To solve this problem, you need to find the \( t \)-value that corresponds to the specified area in the tails of the \( t \)-distribution. Since you have 20 degrees of freedom, and you want the total area to the left of \( -|t| \) and to the right of \( |t| \) to equal 0.1, you need to set each tail's area to 0.05 (since \( 0.1 \div 2 = 0.05 \)). Looking it up in the \( t \)-distribution table for 20 degrees of freedom, you will find that the \( t \)-value that corresponds to an area of 0.05 in the right tail is approximately \( 1.725 \). This means that the values of \( t \) that satisfy your equation are \( -1.725 \) and \( 1.725 \). Remember, as you examine \( t \)-distributions, the shape of these distributions reflects the sample size and degrees of freedom. As the sample size increases, the distribution becomes more similar to the normal distribution. For small samples, those "heavy tails" can really affect the values of \( t \) you get, so vigilant attention to degrees of freedom is key!