To solve this, we need to find the critical value $t$ for a t-distribution with 22 degrees of freedom, where the combined area in the tails (left of $-t$ and right of $t$) equals 0.02.

Steps:

1. Since the combined tail area is 0.02, each tail has an area of $\frac{0.02}{2} = 0.01$.
2. We look up the $t$-value for the upper tail area of 0.01 with 22 degrees of freedom.

Using a t-table or calculator for $t_{0.01, 22}$: $t \approx 2.508$

Thus, the value of $t$ is approximately: $t = 2.508$

Answer:

The value of $t$ is $\boxed{2.508}$.

Would you like further details, or do you have any questions?

Related Questions:

1. How would you find the $t$-value if the degrees of freedom were different?
2. What is the impact of increasing degrees of freedom on the critical $t$-value?
3. How can this method be applied in confidence interval estimation?
4. What is the difference between $t$-distribution and $z$-distribution in hypothesis testing?
5. Why is symmetry important in the t-distribution for this type of calculation?

Tip: For two-tailed tests in a t-distribution, always divide the significance level by two to find the critical value in each tail.