if a sample has 20 observations and a 95% confidence est for a pop is needed. tell me the t- multiple

To find the t-multiple for a 95% confidence interval when the sample has 20 observations, you need to use the **Student's t-distribution**. 

Here's the breakdown:

1. **Degrees of freedom (df)**: For a sample of 20 observations, the degrees of freedom are:
   
   \[
   df = n - 1 = 20 - 1 = 19
   \]

2. **Confidence level**: 95% confidence means that the remaining 5% is split between both tails of the distribution (2.5% in each tail). Hence, you are looking for the critical value that corresponds to the 97.5th percentile of the t-distribution (to cover 95% in the center).

3. **t-multiple**: Looking up the t-distribution table or using a calculator for \( df = 19 \) and a 95% confidence level gives a t-multiple of approximately:

   \[
   t_{0.025, 19} \approx 2.093
   \]

Thus, the **t-multiple is approximately 2.093**.

Would you like further details on the computation, or how to use this value?

### Related Questions
1. How do you construct a confidence interval using the t-multiple?
2. What if the sample size was larger—how does it affect the t-multiple?
3. How does a 99% confidence interval change the t-multiple?
4. Why do we use the t-distribution instead of the normal distribution for small samples?
5. What is the difference between a one-tailed and two-tailed confidence interval?

### Tip:
For samples larger than 30, the t-distribution begins to approximate the normal distribution, and the t-multiple converges to the z-score (like 1.96 for 95% confidence).

Learn how to find the t-multiple for a 95% confidence interval with a sample size of 20 observations. This example covers the Student's t-distribution, degrees of freedom, and calculating critical values. Ideal for college-level statistics students.

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