Find the margin of error for the given values of c, s, and n. c= 0.80, s = 2.5, n=21 Click the icon to view the t-distribution table. ..... The margin of error is . (Round to one decimal place as needed.)
Find the margin of error for the given values of c, s, and n. c= 0.80, s = 2.5, n=21 Click the icon to view the t-distribution table. ..... The margin of error is . (Round to one decimal place as needed.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Calculating the Margin of Error**
To determine the margin of error given certain statistical parameters, consider the following values:
- Confidence level (\(c\)) = 0.80
- Sample standard deviation (\(s\)) = 2.5
- Sample size (\(n\)) = 21
**Step 1: Calculate the Margin of Error**
To find the Margin of Error (ME), use the formula:
\[ \text{ME} = t^* \times \left(\frac{s}{\sqrt{n}}\right) \]
1. **Find the critical value (\(t^*\)):**
Use the t-distribution table with degrees of freedom (\(df = n - 1\)). For this example, \(df = 21 - 1 = 20\).
Given \(c = 0.80\), this corresponds to a 2-tailed probability of 0.20 (i.e., 0.10 in each tail).
2. **Calculate the standard error (SE):**
\[ \text{SE} = \frac{s}{\sqrt{n}} = \frac{2.5}{\sqrt{21}} \]
3. **Substitute the values:**
Multiply \(t^*\) by the calculated SE to find the margin of error.
**Step 2: Rounding Off**
Round the final value of the margin of error to one decimal place as required.
---
**Using the t-Distribution Table**
Select the t-distribution table icon to view and find the critical value \(t^*\), relevant to the calculated degrees of freedom and desired confidence level.
The interface element allows for quick access to statistical tables typically used in student exercises or educational content for accurate analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02fc7836-9552-4a6b-92e4-0fb932880b81%2F95348da3-1ed6-4de7-9cc9-6626518929ee%2Fz5h3vl3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Calculating the Margin of Error**
To determine the margin of error given certain statistical parameters, consider the following values:
- Confidence level (\(c\)) = 0.80
- Sample standard deviation (\(s\)) = 2.5
- Sample size (\(n\)) = 21
**Step 1: Calculate the Margin of Error**
To find the Margin of Error (ME), use the formula:
\[ \text{ME} = t^* \times \left(\frac{s}{\sqrt{n}}\right) \]
1. **Find the critical value (\(t^*\)):**
Use the t-distribution table with degrees of freedom (\(df = n - 1\)). For this example, \(df = 21 - 1 = 20\).
Given \(c = 0.80\), this corresponds to a 2-tailed probability of 0.20 (i.e., 0.10 in each tail).
2. **Calculate the standard error (SE):**
\[ \text{SE} = \frac{s}{\sqrt{n}} = \frac{2.5}{\sqrt{21}} \]
3. **Substitute the values:**
Multiply \(t^*\) by the calculated SE to find the margin of error.
**Step 2: Rounding Off**
Round the final value of the margin of error to one decimal place as required.
---
**Using the t-Distribution Table**
Select the t-distribution table icon to view and find the critical value \(t^*\), relevant to the calculated degrees of freedom and desired confidence level.
The interface element allows for quick access to statistical tables typically used in student exercises or educational content for accurate analysis.
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