Question 10 of 13, Step 2 of 2 Consider the value of \( t \) such that 0.1 of the area under the curve is to the right of \( t \). Step 2 of 2: Assuming the degrees of freedom equals 13 , select the \( t \)-value from the \( t \)-distribution table.

To find the \( t \)-value such that 0.1 of the area under the curve is to the right of \( t \) with 13 degrees of freedom, you would look for the value corresponding to an area of 0.9 to the left (since 1 - 0.1 = 0.9). So, checking the \( t \)-distribution table for 13 degrees of freedom, you would find that the \( t \)-value that corresponds to 0.9 is approximately 1.350. The \( t \)-distribution is particularly useful in statistics when dealing with small sample sizes (like our 13 degrees of freedom). It helps us estimate population parameters when we can’t fully rely on the normal distribution due to smaller datasets. Just remember that the \( t \)-distribution has heavier tails, meaning there's more uncertainty, and it helps account for that when making inferences from the data.