The following data represent the duration of eruptions (in seconds) for a random sample of 10 eruptions of the "Old Faithful" geyser in Yellowstone National Park. 105 119 97 108 125 118 88 107 97 113 a. Assuming all of the necessary conditions are satisfied, create a 96% confidence interval for the mean/average duration of all of Old Faithful's eruptions. (To show your work: Write down which calculator/program you are using and what values you are entering into the calculator.) b. Briefly describe the meaning of your interval from part (b). c. In general, if the size of the sample is increased, will the margin of error become larger, smaller, or stay approximately the same?
The following data represent the duration of eruptions (in seconds) for a random sample of 10 eruptions of the "Old Faithful" geyser in Yellowstone National Park. 105 119 97 108 125 118 88 107 97 113 a. Assuming all of the necessary conditions are satisfied, create a 96% confidence interval for the mean/average duration of all of Old Faithful's eruptions. (To show your work: Write down which calculator/program you are using and what values you are entering into the calculator.) b. Briefly describe the meaning of your interval from part (b). c. In general, if the size of the sample is increased, will the margin of error become larger, smaller, or stay approximately the same?
MATLAB: An Introduction with Applications
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![**Statistical Analysis of "Old Faithful" Geyser Eruption Duration**
*The following data represent the duration of eruptions (in seconds) for a random sample of 10 eruptions of the “Old Faithful” geyser in Yellowstone National Park:*
```
105, 119, 97, 108, 125, 118, 88, 107, 97, 113
```
**Questions:**
**a.** Assuming all of the necessary conditions are satisfied, create a 96% confidence interval for the mean/average duration of all of Old Faithful’s eruptions.
(To show your work: Write down which calculator/program you are using and what values you are entering into the calculator.)
**b.** Briefly describe the meaning of your interval from part (a).
**c.** In general, if the size of the sample is increased, will the margin of error become larger, smaller, or stay approximately the same?
---
**Answer Key and Explanations:**
**a. Calculating the 96% Confidence Interval:**
1. **Find the sample mean (x̄)**:
\[
x̄ = \frac{105 + 119 + 97 + 108 + 125 + 118 + 88 + 107 + 97 + 113}{10} = 107.7 \text{ seconds}
\]
2. **Calculate the sample standard deviation (s)**:
Use your calculator's function to find the sample standard deviation for:
\[
105, 119, 97, 108, 125, 118, 88, 107, 97, 113
\]
Suppose the calculator gives \( s ≈ 11.56 \) seconds.
3. **Determine the standard error (SE)**:
\[
SE = \frac{s}{\sqrt{n}} = \frac{11.56}{\sqrt{10}} ≈ 3.66
\]
4. **Find the critical value (z*) for a 96% confidence level**:
Using a z-table or calculator, \( z* ≈ 2.05 \).
5. **Calculate the margin of error (ME)**:
\[
ME = z* × SE = 2.05 × 3.66 ≈ 7.50
\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2de07fb2-0f01-400d-8693-07014f3d5927%2Fd0a0d48b-b5f4-49b0-9f46-87ecb0f83491%2Fdx2plcm.png&w=3840&q=75)
Transcribed Image Text:**Statistical Analysis of "Old Faithful" Geyser Eruption Duration**
*The following data represent the duration of eruptions (in seconds) for a random sample of 10 eruptions of the “Old Faithful” geyser in Yellowstone National Park:*
```
105, 119, 97, 108, 125, 118, 88, 107, 97, 113
```
**Questions:**
**a.** Assuming all of the necessary conditions are satisfied, create a 96% confidence interval for the mean/average duration of all of Old Faithful’s eruptions.
(To show your work: Write down which calculator/program you are using and what values you are entering into the calculator.)
**b.** Briefly describe the meaning of your interval from part (a).
**c.** In general, if the size of the sample is increased, will the margin of error become larger, smaller, or stay approximately the same?
---
**Answer Key and Explanations:**
**a. Calculating the 96% Confidence Interval:**
1. **Find the sample mean (x̄)**:
\[
x̄ = \frac{105 + 119 + 97 + 108 + 125 + 118 + 88 + 107 + 97 + 113}{10} = 107.7 \text{ seconds}
\]
2. **Calculate the sample standard deviation (s)**:
Use your calculator's function to find the sample standard deviation for:
\[
105, 119, 97, 108, 125, 118, 88, 107, 97, 113
\]
Suppose the calculator gives \( s ≈ 11.56 \) seconds.
3. **Determine the standard error (SE)**:
\[
SE = \frac{s}{\sqrt{n}} = \frac{11.56}{\sqrt{10}} ≈ 3.66
\]
4. **Find the critical value (z*) for a 96% confidence level**:
Using a z-table or calculator, \( z* ≈ 2.05 \).
5. **Calculate the margin of error (ME)**:
\[
ME = z* × SE = 2.05 × 3.66 ≈ 7.50
\
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