Suppose we are making a 99% confidence interval for the population mean from a sample size 17. What number of degrees of freedom should we use?

The number of degrees of freedom is:   

When constructing a confidence interval for the population mean using a sample, the number of degrees of freedom (df) is calculated as:

\[
\text{df} = n - 1
\]

Where \(n\) is the sample size.

Given:
- Sample size \(n = 17\)

So, the number of degrees of freedom would be:

\[
\text{df} = 17 - 1 = 16
\]

Thus, the number of degrees of freedom is **16**.

Would you like to explore more details or have any questions?

Here are some related questions you might explore:
1. Why do we subtract 1 from the sample size to find the degrees of freedom?
2. How does the degrees of freedom affect the t-distribution?
3. How does sample size impact the width of a confidence interval?
4. What would be the degrees of freedom for a sample size of 30?
5. How does the confidence level affect the critical value in a t-distribution?
6. What is the difference between using a t-distribution and a z-distribution?
7. How does the t-distribution change as the degrees of freedom increase?
8. What would be the effect of a small sample size on the accuracy of the confidence interval?

**Tip:** Always remember that the degrees of freedom are crucial when using the t-distribution, especially for small sample sizes. The t-distribution accounts for the extra uncertainty introduced by estimating the population standard deviation from the sample.

Understand how to calculate the degrees of freedom when constructing a 99% confidence interval for a population mean from a sample size of 17. Learn the formula and its application in statistical inference.

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