Question 1165660
To find the two $t$-values that define the middle $0.95$ area of a $t$-distribution with $df=27$, you are looking for the critical values, $\pm t_{\alpha/2}$. 

In this case:

* The area in the middle is **0.95**.
* The total area in the two tails is $1 - 0.95 = 0.05$.
* The area in each individual tail ($\alpha/2$) is $0.05 / 2 = \mathbf{0.025}$.
* The **degrees of freedom ($df$)** are **27**.

You need to find the $t$-value such that the area to the right of it is $0.025$. This value is often denoted as $t_{0.025, 27}$.

Using a $t$-distribution table or calculator for a two-tailed $95\%$ confidence level with $df=27$:

$$\mathbf{t_{\text{critical}} \approx 2.052}$$

Therefore, the two $t$-values that divide the area under the curve are $\mathbf{-2.052}$ and $\mathbf{+2.052}$.