Suppose that Sandy is an analyst for the bicyling industry and wants to estimate the asking price of used entry-level road bikes advertised online in the southeastern part of the United States. She obtains a random sample of n = 10 online advertisements of entry-level road bikes. She determines that the mean price for these 10 bikes is $659.87 and that the sample standard deviation is s = $197.02. She uses this information to construct a 95% confidence interval for u, the mean price of a used road bike. What is the upper limit of this confidence interval? Please give your answer to the nearest cent.
Suppose that Sandy is an analyst for the bicyling industry and wants to estimate the asking price of used entry-level road bikes advertised online in the southeastern part of the United States. She obtains a random sample of n = 10 online advertisements of entry-level road bikes. She determines that the mean price for these 10 bikes is $659.87 and that the sample standard deviation is s = $197.02. She uses this information to construct a 95% confidence interval for u, the mean price of a used road bike. What is the upper limit of this confidence interval? Please give your answer to the nearest cent.
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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![**Estimation of the Asking Price of Used Entry-Level Road Bikes**
**Problem Statement:**
Sandy, an analyst in the bicycling industry, aims to estimate the asking price of used entry-level road bikes advertised online in the southeastern part of the United States. She collects a random sample of \( n = 10 \) online advertisements for entry-level road bikes. From this sample, Sandy determines that the mean price is \( \$659.87 \) and the sample standard deviation is \( s = \$197.02 \). Sandy utilizes this data to construct a 95% confidence interval for \( \mu \), the mean price of a used road bike.
**Question:**
What is the upper limit of this confidence interval? Please provide your answer to the nearest cent.
**Solution Framework:**
To find the confidence interval, Sandy will use the formula for the confidence interval for the mean:
\[ \text{CI} = \bar{x} \pm t_{\alpha/2} \left( \frac{s}{\sqrt{n}} \right) \]
Where:
- \( \bar{x} \) is the sample mean.
- \( t_{\alpha/2} \) is the t-value for the 95% confidence level with \( n-1 \) degrees of freedom.
- \( s \) is the sample standard deviation.
- \( n \) is the sample size.
Given the sample size of 10, Sandy will use the t-distribution to find the critical value \( t_{\alpha/2} \). Since the sample size is small (n < 30), using the t-distribution is appropriate for better accuracy compared to the z-distribution.
After calculating the values, the upper limit of the confidence interval will give us the higher end of the estimated range for the mean price of these used bikes.
**Graph/Diagram Explanation:**
There are no graphs or diagrams associated with this text. All necessary calculations can be carried out using statistical tables or computational tools to find the required t-value for constructing the confidence interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c238f55-55d8-4646-a51d-6e566d674b1c%2Fada08d31-cca2-4d8c-b169-2eec5ad90cb9%2Furssoyp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Estimation of the Asking Price of Used Entry-Level Road Bikes**
**Problem Statement:**
Sandy, an analyst in the bicycling industry, aims to estimate the asking price of used entry-level road bikes advertised online in the southeastern part of the United States. She collects a random sample of \( n = 10 \) online advertisements for entry-level road bikes. From this sample, Sandy determines that the mean price is \( \$659.87 \) and the sample standard deviation is \( s = \$197.02 \). Sandy utilizes this data to construct a 95% confidence interval for \( \mu \), the mean price of a used road bike.
**Question:**
What is the upper limit of this confidence interval? Please provide your answer to the nearest cent.
**Solution Framework:**
To find the confidence interval, Sandy will use the formula for the confidence interval for the mean:
\[ \text{CI} = \bar{x} \pm t_{\alpha/2} \left( \frac{s}{\sqrt{n}} \right) \]
Where:
- \( \bar{x} \) is the sample mean.
- \( t_{\alpha/2} \) is the t-value for the 95% confidence level with \( n-1 \) degrees of freedom.
- \( s \) is the sample standard deviation.
- \( n \) is the sample size.
Given the sample size of 10, Sandy will use the t-distribution to find the critical value \( t_{\alpha/2} \). Since the sample size is small (n < 30), using the t-distribution is appropriate for better accuracy compared to the z-distribution.
After calculating the values, the upper limit of the confidence interval will give us the higher end of the estimated range for the mean price of these used bikes.
**Graph/Diagram Explanation:**
There are no graphs or diagrams associated with this text. All necessary calculations can be carried out using statistical tables or computational tools to find the required t-value for constructing the confidence interval.
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