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The question asks for the **critical t-value** for a **95% confidence level** with a **sample size of 27**.

To find the critical t-value, follow these steps:

1. Determine the degrees of freedom (df). For a t-distribution, the degrees of freedom are calculated as:

\[
df = n - 1 = 27 - 1 = 26
\]

2. For a 95% confidence level, the critical t-value corresponds to a tail probability of \( \alpha = 0.05 \), with 0.025 in each tail (since the t-distribution is symmetric).

3. Using a t-distribution table or calculator for **df = 26** and a **confidence level of 95%**, the critical t-value is approximately **2.056**.

Thus, the critical t-value is **2.056**.

Would you like to explore how to find critical values using a t-distribution table or online calculator? Let me know if you need further clarification!

### Related Questions:
1. What is the critical t-value for a 99% confidence level with the same sample size?
2. How do confidence intervals differ between t-distribution and z-distribution?
3. How do degrees of freedom affect the critical t-value?
4. Can you explain why the t-distribution is used instead of the z-distribution in small samples?
5. What happens to the critical t-value as the sample size increases?

#### Tip:
Always remember that as the sample size increases, the t-distribution approaches the standard normal (z) distribution, meaning the t-values get closer to z-values.

For a confidence level of 95% with a sample size of 27, find the critical t-value.

Learn how to calculate the critical t-value for a 95% confidence level using a sample size of 27. This problem covers key statistical concepts such as degrees of freedom, t-distribution, and confidence intervals.

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