Consider the value of t such that 0.01
 of the area under the curve is to the right of t.  

Step 2 of 2 :  Assuming the degrees of freedom equals 21
, select the t-value from the t-distribution table.

To find the \( t \)-value such that 0.01 of the area under the curve lies to the right of \( t \), we’ll refer to the **t-distribution** with **21 degrees of freedom**.

Since 0.01 of the area lies to the right, this corresponds to finding the 99th percentile (0.99) on the **t-distribution table** for 21 degrees of freedom.

Looking up the 99th percentile for 21 degrees of freedom:
\[
t_{0.99, 21} \approx 2.518
\]

Thus, the \( t \)-value is approximately **2.518**.

Would you like further details on how to use the t-distribution table, or do you have any other questions?

Here are five related questions to explore this concept further:
1. What would the \( t \)-value be if 0.05 of the area were to the right of \( t \) with 21 degrees of freedom?
2. How does the \( t \)-value change with increasing or decreasing degrees of freedom?
3. What is the difference between using a t-distribution and a normal distribution in hypothesis testing?
4. Can you explain why we use the 99th percentile in this case instead of another percentile?
5. How would you find a \( t \)-value if only given cumulative probabilities?

**Tip:** The t-distribution approaches the normal distribution as degrees of freedom increase, typically beyond 30.

Consider the value of t such that 0.01 of the area under the curve is to the right of t. Assuming the degrees of freedom equals 21, select the t-value from the t-distribution table.

Learn how to find the t-value for a 0.01 area under the curve to the right with 21 degrees of freedom using the t-distribution table. This solution covers key concepts in statistics, including the t-distribution, percentiles, and degrees of freedom. Ideal for college-level statistics students.

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