Find the margin of error for the given values of c, s, and n. c=0.99, s=2.1, n=17 Click the icon to view the t-distribution table. The margin of error is. (Round to one decimal place as needed.) t-Distribution Table d.f. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Level of confidence, c 0.80 One tail, a Two tails, a 0.90 0.95 0.98 0.99 0.10 0.05 0.025 0.01 0.005 0.20 0.10 0.05 0.02 0.01 d.f. 3.078 6.314 12.706 31.821 63.657 1 1.886 2.920 4.303 6.965 9.925 2 1.638 2.353 3.182 4.541 5.841 3 1.533 2.132 2.776 3.747 4.604 4 1.476 2.015 2.571 3.365 4.032 5 1.440 1.943 2.447 3.143 3.707 6 1.415 1.895 2.365 2.998 3.499 7 1.397 1.860 2.306 2.896 3.355 8 1.383 1.833 2.262 2.821 3.250 9 1.372 1.812 2.228 2.764 3.169 10 1.363 1.796 2.201 2.718 3.106 11 1.356 1.782 2.179 2.681 3.055 12 1.350 1.771 2.160 2.650 3.012 13 1.345 1.761 2.145 2.624 2.977 1.341 1.753 2.131 2.602 2.947 1.337 1.746 2.120 2.583 2.921 1.333 1.740 2.110 2.567 2.898 1.330 1.734 2.101 2.552 2.878 18 1.328 1.729 2.093 2.539 2.861 19 1.325 1.725 2.086 2.528 2.845 20 1.323 1.721 2.080 2.518 2.831 21 1.321 1.717 2.074 2.508 2.819 22 1.319 1.714 2.069 2.500 2.807 23 2.492 2.797 24 2.485 2.787 25 14 15 16 17 1.318 1.316 1.711 2.064 1.708 2.060 - X
Find the margin of error for the given values of c, s, and n. c=0.99, s=2.1, n=17 Click the icon to view the t-distribution table. The margin of error is. (Round to one decimal place as needed.) t-Distribution Table d.f. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Level of confidence, c 0.80 One tail, a Two tails, a 0.90 0.95 0.98 0.99 0.10 0.05 0.025 0.01 0.005 0.20 0.10 0.05 0.02 0.01 d.f. 3.078 6.314 12.706 31.821 63.657 1 1.886 2.920 4.303 6.965 9.925 2 1.638 2.353 3.182 4.541 5.841 3 1.533 2.132 2.776 3.747 4.604 4 1.476 2.015 2.571 3.365 4.032 5 1.440 1.943 2.447 3.143 3.707 6 1.415 1.895 2.365 2.998 3.499 7 1.397 1.860 2.306 2.896 3.355 8 1.383 1.833 2.262 2.821 3.250 9 1.372 1.812 2.228 2.764 3.169 10 1.363 1.796 2.201 2.718 3.106 11 1.356 1.782 2.179 2.681 3.055 12 1.350 1.771 2.160 2.650 3.012 13 1.345 1.761 2.145 2.624 2.977 1.341 1.753 2.131 2.602 2.947 1.337 1.746 2.120 2.583 2.921 1.333 1.740 2.110 2.567 2.898 1.330 1.734 2.101 2.552 2.878 18 1.328 1.729 2.093 2.539 2.861 19 1.325 1.725 2.086 2.528 2.845 20 1.323 1.721 2.080 2.518 2.831 21 1.321 1.717 2.074 2.508 2.819 22 1.319 1.714 2.069 2.500 2.807 23 2.492 2.797 24 2.485 2.787 25 14 15 16 17 1.318 1.316 1.711 2.064 1.708 2.060 - X
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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![### Finding the Margin of Error
To find the margin of error for the given values of \( c \), \( s \), and \( n \):
Given:
- \( c \) (confidence level) = 0.99
- \( s \) (sample standard deviation) = 2.1
- \( n \) (sample size) = 17
**Step 1:** Click the icon to view the t-distribution table.
### t-Distribution Table
The t-distribution table is a statistical table that shows the critical values of the t-distribution. The table is organized as follows:
- **Levels of confidence (\( c \))**: 0.80, 0.90, 0.95, 0.98, and 0.99.
- **Degrees of freedom (\( \text{d.f.} \))**: The number of values in the final calculation of a statistic that are free to vary.
For each combination of confidence level and degrees of freedom, the table provides the t-values to be used in statistical calculations.
Example rows include:
- For \( \text{d.f.} = 1 \):
- \( c = 0.80 \rightarrow \text{t-value} = 3.078 \)
- \( c = 0.99 \rightarrow \text{t-value} = 31.821 \)
- For \( \text{d.f.} = 17 \):
- \( c = 0.80 \rightarrow \text{t-value} = 1.333 \)
- \( c = 0.99 \rightarrow \text{t-value} = 2.898 \)
**Step 2:** With \( n = 17 \), the degrees of freedom (\( \text{d.f.} \)) are \( n - 1 = 16 \).
Looking at the row for \( \text{d.f.} = 16 \) under the column for \( c = 0.99 \):
- The t-value is 2.921.
**Step 3:** Calculate the margin of error.
\[
\text{Margin of Error} = t \times \left( \frac{s}{\sqrt{n}} \right)
\]
Substitute the values:
\[
\text{Margin of Error} = 2.921 \times \left( \frac](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a5e68af-43fc-4f18-979d-78274e50dd4a%2F4ecc76f4-5ca1-493e-a206-cdb3e9926798%2Fewhdexv_processed.png&w=3840&q=75)
Transcribed Image Text:### Finding the Margin of Error
To find the margin of error for the given values of \( c \), \( s \), and \( n \):
Given:
- \( c \) (confidence level) = 0.99
- \( s \) (sample standard deviation) = 2.1
- \( n \) (sample size) = 17
**Step 1:** Click the icon to view the t-distribution table.
### t-Distribution Table
The t-distribution table is a statistical table that shows the critical values of the t-distribution. The table is organized as follows:
- **Levels of confidence (\( c \))**: 0.80, 0.90, 0.95, 0.98, and 0.99.
- **Degrees of freedom (\( \text{d.f.} \))**: The number of values in the final calculation of a statistic that are free to vary.
For each combination of confidence level and degrees of freedom, the table provides the t-values to be used in statistical calculations.
Example rows include:
- For \( \text{d.f.} = 1 \):
- \( c = 0.80 \rightarrow \text{t-value} = 3.078 \)
- \( c = 0.99 \rightarrow \text{t-value} = 31.821 \)
- For \( \text{d.f.} = 17 \):
- \( c = 0.80 \rightarrow \text{t-value} = 1.333 \)
- \( c = 0.99 \rightarrow \text{t-value} = 2.898 \)
**Step 2:** With \( n = 17 \), the degrees of freedom (\( \text{d.f.} \)) are \( n - 1 = 16 \).
Looking at the row for \( \text{d.f.} = 16 \) under the column for \( c = 0.99 \):
- The t-value is 2.921.
**Step 3:** Calculate the margin of error.
\[
\text{Margin of Error} = t \times \left( \frac{s}{\sqrt{n}} \right)
\]
Substitute the values:
\[
\text{Margin of Error} = 2.921 \times \left( \frac
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