The problem asks you to find the probability $P(T > 2.42)$ for a t-distribution with 12 degrees of freedom.

To solve this:

1. We need to find the cumulative probability for the t-value $T = 2.42$ using the t-distribution table or a calculator.
2. We will subtract this cumulative probability from 1 to get $P(T > 2.42)$.

Steps:

• Use a t-distribution table or a calculator that can handle t-distributions to find $P(T \leq 2.42)$ for 12 degrees of freedom.

• Once you have the value $P(T \leq 2.42)$, subtract it from 1:

  $P(T > 2.42) = 1 - P(T \leq 2.42)$

Using a calculator or a tool like Excel:

You can calculate this value using an online t-distribution calculator or software like Excel. In Excel, you would use:

excelCopy code
=TDIST(2.42, 12, 1)

This will give you the one-tailed p-value for $P(T > 2.42)$.

Would you like a detailed breakdown of these calculations or further clarification?

Here are 5 related questions:

1. What is a t-distribution, and when is it used instead of a normal distribution?
2. How do you calculate probabilities using a t-distribution table manually?
3. What is the relationship between degrees of freedom and the shape of the t-distribution?
4. How do you interpret the p-value in the context of hypothesis testing?
5. How does the result change if we change the degrees of freedom?

Tip: Remember, the larger the degrees of freedom, the closer the t-distribution approximates the normal distribution.