An adviser in student services would like to estimate the average monthly car payment of all IRSC students. From past research, it is known that the standard deviation of the distribution of all IRSC student car payments is $41. Determine the sample size necessary such that the margin of error of the estimate for a 99% confidence interval for the average monthly car payment of all IRSC students is at most $6.29. Round the solution up to the nearest whole number. N=
An adviser in student services would like to estimate the average monthly car payment of all IRSC students. From past research, it is known that the standard deviation of the distribution of all IRSC student car payments is $41. Determine the sample size necessary such that the margin of error of the estimate for a 99% confidence interval for the average monthly car payment of all IRSC students is at most $6.29. Round the solution up to the nearest whole number. N=
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
#5). Need help solving.
![### Sample Size Determination for Estimating Average Monthly Car Payments of IRSC Students
An adviser in student services is tasked with estimating the average monthly car payment for all IRSC (Indian River State College) students. Based on past research, it is known that the standard deviation of the distribution of all IRSC student car payments is $41.
The objective is to determine the necessary sample size such that the margin of error for the estimate within a 99% confidence interval is at most $6.29. The solution should be rounded up to the nearest whole number.
\[ n = \_\_\_\_\_\_ \]
**Steps to Calculate Sample Size:**
1. **Identify the Standard Deviation (σ):**
\[ \sigma = 41 \]
2. **Determine the Margin of Error (E):**
\[ E = 6.29 \]
3. **Find the Z-value for 99% Confidence Level (Z):**
- For a 99% confidence level, the Z-value (Z) is approximately 2.576 (you can find this value using a Z-table).
4. **Sample Size Formula:**
\[ n = \left( \frac{Z \cdot \sigma}{E} \right)^2 \]
5. **Plug in the Values:**
\[ n = \left( \frac{2.576 \cdot 41}{6.29} \right)^2 \]
6. **Calculate the Sample Size:**
\[
\begin{align*}
n & = \left( \frac{105.616}{6.29} \right)^2 \\
n & = \left( 16.8 \right)^2 \\
n & = 282.24
\end{align*}
\]
Round up 282.24 to the nearest whole number:
\[ n = 283 \]
Therefore, to estimate the average monthly car payment of all IRSC students with a margin of error of $6.29 at a 99% confidence level, a sample size of 283 students is required.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F090c748e-ae6e-4835-a77f-8d1d8bf06681%2Fb81e4cdd-22dd-4814-965f-e7738cb4898c%2Fr9ee2l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Sample Size Determination for Estimating Average Monthly Car Payments of IRSC Students
An adviser in student services is tasked with estimating the average monthly car payment for all IRSC (Indian River State College) students. Based on past research, it is known that the standard deviation of the distribution of all IRSC student car payments is $41.
The objective is to determine the necessary sample size such that the margin of error for the estimate within a 99% confidence interval is at most $6.29. The solution should be rounded up to the nearest whole number.
\[ n = \_\_\_\_\_\_ \]
**Steps to Calculate Sample Size:**
1. **Identify the Standard Deviation (σ):**
\[ \sigma = 41 \]
2. **Determine the Margin of Error (E):**
\[ E = 6.29 \]
3. **Find the Z-value for 99% Confidence Level (Z):**
- For a 99% confidence level, the Z-value (Z) is approximately 2.576 (you can find this value using a Z-table).
4. **Sample Size Formula:**
\[ n = \left( \frac{Z \cdot \sigma}{E} \right)^2 \]
5. **Plug in the Values:**
\[ n = \left( \frac{2.576 \cdot 41}{6.29} \right)^2 \]
6. **Calculate the Sample Size:**
\[
\begin{align*}
n & = \left( \frac{105.616}{6.29} \right)^2 \\
n & = \left( 16.8 \right)^2 \\
n & = 282.24
\end{align*}
\]
Round up 282.24 to the nearest whole number:
\[ n = 283 \]
Therefore, to estimate the average monthly car payment of all IRSC students with a margin of error of $6.29 at a 99% confidence level, a sample size of 283 students is required.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman