Find the value of t for a t-distribution with 50 degrees of freedom such that the area to the right of t equals 0.005. Round your answer to three decimal places, if necessary.

Answer:

Step 1: Given Data

We are provided with the following:

• Degrees of freedom, $df=50$
• The area to the right of $t$ is $0.005$

We are tasked with finding the value of $t$ such that $P(t>t_{0.005})=0.005$.

Step 2: Finding the Critical Value

The value of $t$ such that the area to the right of $t$ equals 0.005 can be calculated using the following steps:

$P(t>t_{0.005})=0.005$

The area to the left of $t$ is:

$P(t<t_{0.005})=1–0.005=0.995$

We can use the Excel function =T.INV(0.995, 50) to find the critical value. This gives us:

$t_c=2.678$

Final Solution:

The critical value of $t$ for the given area is:

$t=2.678$