Find the t-value such that the area left of the t-value is 0.25 with 22 degrees of freedom.
(Round to three decimal olaces as needed)

Step 1 ：We are asked to find the t-value such that the area left of the t-value is 0.25 with 22 degrees of freedom. This is equivalent to finding the 25th percentile of the t-distribution with 22 degrees of freedom.

Step 2 ：We can use the Percent Point Function (PPF), which is the inverse of the Cumulative Distribution Function (CDF), to find this t-value. The PPF gives the value of the variable for a given percentile.

Step 3 ：Let's denote the degrees of freedom as \(df\) and the percentile as \(p\). In this case, \(df = 22\) and \(p = 0.25\).

Step 4 ：By using the PPF, we find that the t-value is approximately -0.686.

Step 5 ：Final Answer: The t-value such that the area left of the t-value is 0.25 with 22 degrees of freedom is \(\boxed{-0.686}\).