Find the margin of error for the given values of c, s, and n. c= 0.80, s = 3.9, n = 9 Click the icon to view the t-distribution table. The margin of error is (Round to one decimal place as needed.)

MATLAB: An Introduction with Applications
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**Finding the Margin of Error Using a T-Distribution**

To calculate the margin of error for a set of data, given the values of c (confidence level), s (sample standard deviation), and n (sample size), follow these steps:

**Given Values:**
- Confidence level, \( c = 0.80 \)
- Sample standard deviation, \( s = 3.9 \)
- Sample size, \( n = 9 \)

**Step-by-Step Process:**

1. **Determine the degrees of freedom (df):**
   \[
   df = n - 1 = 9 - 1 = 8
   \]

2. **Find the critical value (t) using the t-distribution table:**
   - Use the t-distribution table to find the critical t-value for a confidence level of 0.80 and 8 degrees of freedom.

3. **Calculate the margin of error (ME) using the formula:**
   \[
   ME = t \times \frac{s}{\sqrt{n}}
   \]

4. **Round the final result to one decimal place as needed.**

This process provides the margin of error, which is crucial to assess the range within which the true population parameter is expected to fall with the specified confidence level.

**Note:**
To find step 2 in detail, click the icon to view the t-distribution table. Proper application of this method ensures accuracy in statistical analysis and confidence interval estimation.
Transcribed Image Text:**Finding the Margin of Error Using a T-Distribution** To calculate the margin of error for a set of data, given the values of c (confidence level), s (sample standard deviation), and n (sample size), follow these steps: **Given Values:** - Confidence level, \( c = 0.80 \) - Sample standard deviation, \( s = 3.9 \) - Sample size, \( n = 9 \) **Step-by-Step Process:** 1. **Determine the degrees of freedom (df):** \[ df = n - 1 = 9 - 1 = 8 \] 2. **Find the critical value (t) using the t-distribution table:** - Use the t-distribution table to find the critical t-value for a confidence level of 0.80 and 8 degrees of freedom. 3. **Calculate the margin of error (ME) using the formula:** \[ ME = t \times \frac{s}{\sqrt{n}} \] 4. **Round the final result to one decimal place as needed.** This process provides the margin of error, which is crucial to assess the range within which the true population parameter is expected to fall with the specified confidence level. **Note:** To find step 2 in detail, click the icon to view the t-distribution table. Proper application of this method ensures accuracy in statistical analysis and confidence interval estimation.
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