To find the critical values for a t-distribution, follow these steps:

Step 1: Identify the level of significance ($\alpha$) and the degrees of freedom (d.f.)

• The degrees of freedom (d.f.) are calculated as $d.f. = n - 1$, where $n$ is the sample size.
• The level of significance ($\alpha$) is the probability threshold used for testing your hypothesis. This is typically given in the problem (e.g., 0.05, 0.01).

So, the correct answer to the first step is:

A. Identify the level of significance $\alpha$ and the degrees of freedom, d.f. = n - 1.

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Step 2: Find the critical value using the t-distribution table.

Once you know the level of significance and the degrees of freedom, you can look up the critical value(s) in the t-distribution table:

• For a left-tailed test, look up the value in the column corresponding to $\alpha$ and the row with your calculated degrees of freedom.
• For a right-tailed test, use the value that corresponds to $1 - \alpha$ in the table.
• For a two-tailed test, divide $\alpha$ by 2 (i.e., use $\alpha/2$) and find the corresponding value.

Would you like me to explain the next steps or anything in more detail? Or do you have a specific problem you'd like help with?

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Here are 5 follow-up questions to help you understand critical values and hypothesis testing:

1. How do you determine whether a hypothesis test is left-tailed, right-tailed, or two-tailed?
2. What does the degrees of freedom represent in a t-distribution, and why is it calculated as $n - 1$?
3. How do you use the t-distribution table for a two-tailed hypothesis test?
4. Can you explain how to interpret a critical value for a left-tailed test using the t-distribution?
5. What happens if the significance level $\alpha$ is different in a hypothesis test?

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Tip: Make sure to always check whether your hypothesis test is one-tailed or two-tailed, as it affects which column of the t-distribution table you use!