Which distribution should you use for this problem? (Enter your answer in the form z or tgr where df is the degrees of freedom.) Explain your choice. O The Student's t-distribution for 14 degrees of freedom should be used because the sample standard deviation is known. The standard normal distribution should be used because the sample standard deviation is known. O The standard normal distribution should be used because the population standard deviation is known. O The Student's t-distribution for 13 degrees of freedom should be used because we do not know the population standard deviation. = Part (e) Construct a 99% confidence interval for the population mean length of time using training wheels. () State the confidence interval. (Round your answers to two decimal places.) (H) Sketch the graph. (Round your answers to two decimal places. Enter your al2 to three decimal places.) (H1) Calculate the error bound. (Round your answer to two decimal places.) Customize and control Google Chrome = Part (1) () Why would the error bound change if the confidence level were lowered to 90%? O When the confidence level changes, the interval does not change. O When the confidence level decreases, the error bound for the confidence interval decreases as well. O When the confidence level increases, the error bound for the confidence interval increases as well. IX 비2 비2
Which distribution should you use for this problem? (Enter your answer in the form z or tgr where df is the degrees of freedom.) Explain your choice. O The Student's t-distribution for 14 degrees of freedom should be used because the sample standard deviation is known. The standard normal distribution should be used because the sample standard deviation is known. O The standard normal distribution should be used because the population standard deviation is known. O The Student's t-distribution for 13 degrees of freedom should be used because we do not know the population standard deviation. = Part (e) Construct a 99% confidence interval for the population mean length of time using training wheels. () State the confidence interval. (Round your answers to two decimal places.) (H) Sketch the graph. (Round your answers to two decimal places. Enter your al2 to three decimal places.) (H1) Calculate the error bound. (Round your answer to two decimal places.) Customize and control Google Chrome = Part (1) () Why would the error bound change if the confidence level were lowered to 90%? O When the confidence level changes, the interval does not change. O When the confidence level decreases, the error bound for the confidence interval decreases as well. O When the confidence level increases, the error bound for the confidence interval increases as well. IX 비2 비2
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
Suppose that 14 children, who were learning to ride two-wheel bikes, were surveyed to determine how long they had to use training wheels. It was revealed that they used them an average of ten months with a sample standard deviation of five months. Assume that the underlying population distribution is normal.
![**Distribution Selection and Confidence Interval Construction**
**Distribution Selection:**
Which distribution should you use for this problem? (Enter your answer in the form \( z \) or \( t_{df} \) where \( df \) is the degrees of freedom.)
[Answer Box]
**Explain your choice:**
- \( \circ \) The Student’s \( t \)-distribution for 14 degrees of freedom should be used because the sample standard deviation is known.
- \( \circ \) The standard normal distribution should be used because the sample standard deviation is known.
- \( \circ \) The standard normal distribution should be used because the population standard deviation is known.
- \( \circ \) The Student’s \( t \)-distribution for 13 degrees of freedom should be used because we do not know the population standard deviation.
---
**Part (e): Confidence Interval Construction:**
Construct a 99% confidence interval for the population mean length of time using training wheels.
**(i) State the confidence interval.** (Round your answers to two decimal places.)
(\[ \text{Lower Bound} \], \[ \text{Upper Bound} \])
**(ii) Sketch the graph.** (Round your answers to two decimal places. Enter your \( \alpha/2 \) to three decimal places.)
- Sketch shows a normal distribution curve.
- Central region labeled "CL = [Confidence Level Box]"
- Ends of the curve labeled \( \alpha/2 = \) [Left Box] and \( \alpha/2 = \) [Right Box]
- \( \overline{x} \) marked at the center of the curve with arrows pointing to boundaries of confidence interval
**(iii) Calculate the error bound.** (Round your answer to two decimal places.)
[Error Bound Box]
---
**Part (f): Impact of Confidence Level on Error Bound**
(f) Why would the error bound change if the confidence level were lowered to 90%?
- \( \circ \) When the confidence level changes, the interval does not change.
- \( \circ \) When the confidence level decreases, the error bound for the confidence interval decreases as well.
- \( \circ \) When the confidence level increases, the error bound for the confidence interval increases as well.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F692b4a3d-b328-4d6d-8f5c-2ba3aed54605%2F617286f9-02e1-413e-9467-0b9dd14ffe23%2F9sk5l13_processed.png&w=3840&q=75)
Transcribed Image Text:**Distribution Selection and Confidence Interval Construction**
**Distribution Selection:**
Which distribution should you use for this problem? (Enter your answer in the form \( z \) or \( t_{df} \) where \( df \) is the degrees of freedom.)
[Answer Box]
**Explain your choice:**
- \( \circ \) The Student’s \( t \)-distribution for 14 degrees of freedom should be used because the sample standard deviation is known.
- \( \circ \) The standard normal distribution should be used because the sample standard deviation is known.
- \( \circ \) The standard normal distribution should be used because the population standard deviation is known.
- \( \circ \) The Student’s \( t \)-distribution for 13 degrees of freedom should be used because we do not know the population standard deviation.
---
**Part (e): Confidence Interval Construction:**
Construct a 99% confidence interval for the population mean length of time using training wheels.
**(i) State the confidence interval.** (Round your answers to two decimal places.)
(\[ \text{Lower Bound} \], \[ \text{Upper Bound} \])
**(ii) Sketch the graph.** (Round your answers to two decimal places. Enter your \( \alpha/2 \) to three decimal places.)
- Sketch shows a normal distribution curve.
- Central region labeled "CL = [Confidence Level Box]"
- Ends of the curve labeled \( \alpha/2 = \) [Left Box] and \( \alpha/2 = \) [Right Box]
- \( \overline{x} \) marked at the center of the curve with arrows pointing to boundaries of confidence interval
**(iii) Calculate the error bound.** (Round your answer to two decimal places.)
[Error Bound Box]
---
**Part (f): Impact of Confidence Level on Error Bound**
(f) Why would the error bound change if the confidence level were lowered to 90%?
- \( \circ \) When the confidence level changes, the interval does not change.
- \( \circ \) When the confidence level decreases, the error bound for the confidence interval decreases as well.
- \( \circ \) When the confidence level increases, the error bound for the confidence interval increases as well.
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