An important factor in selling a residential property is the number of people who look through the home. A sample of 19 homes recently sold in the Buffalo, New York, area revealed the mean number looking through each home was 27 and the standard deviation of the sample was 6 people. Develop a 95% confidence interval for the population mean. (Use t Distribution Table.) (Round your answers to 2 decimal places.)
An important factor in selling a residential property is the number of people who look through the home. A sample of 19 homes recently sold in the Buffalo, New York, area revealed the mean number looking through each home was 27 and the standard deviation of the sample was 6 people. Develop a 95% confidence interval for the population mean. (Use t Distribution Table.) (Round your answers to 2 decimal places.)
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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![### Determining the Confidence Interval for Population Mean
An essential factor in selling a residential property is the number of people who look through the home. A sample of 19 homes recently sold in the Buffalo, New York, area revealed the mean number looking through each home was 27 and the standard deviation of the sample was 6 people.
**Objective:**
Develop a 95% confidence interval for the population mean (use the t Distribution Table).
**Instructions:**
Round your answers to 2 decimal places.
**Confidence Interval Calculation:**
For this task, you will need to:
1. Calculate the sample mean (given as 27).
2. Determine the standard deviation (given as 6).
3. Identify the sample size (19 homes).
4. Use the t Distribution Table to find the t-value for a 95% confidence level with n-1 degrees of freedom (where n is the sample size).
5. Use the following formula to calculate the confidence interval:
\[
\text{Confidence Interval} = \bar{x} \pm \left(t_{\alpha/2} \times \frac{s}{\sqrt{n}}\right)
\]
where:
- \(\bar{x}\) is the sample mean,
- \(t_{\alpha/2}\) is the t-value for the desired confidence level,
- \(s\) is the sample standard deviation,
- \(n\) is the sample size.
Using these steps and the provided data, you can calculate and find the confidence interval.
**Graphical Representation:**
There is a rectangular table included in the image to record the calculated confidence interval.
**Table:**
| Confidence Interval for the Population Mean is between | [ ] | and | [ ] |
This is where your calculated lower and upper limits of the confidence interval should be written after performing the above calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2afe4021-ca35-45b6-a0c9-c497a9a18abf%2F283398a6-7317-41a6-b137-d4f50949a393%2F4umigcn.png&w=3840&q=75)
Transcribed Image Text:### Determining the Confidence Interval for Population Mean
An essential factor in selling a residential property is the number of people who look through the home. A sample of 19 homes recently sold in the Buffalo, New York, area revealed the mean number looking through each home was 27 and the standard deviation of the sample was 6 people.
**Objective:**
Develop a 95% confidence interval for the population mean (use the t Distribution Table).
**Instructions:**
Round your answers to 2 decimal places.
**Confidence Interval Calculation:**
For this task, you will need to:
1. Calculate the sample mean (given as 27).
2. Determine the standard deviation (given as 6).
3. Identify the sample size (19 homes).
4. Use the t Distribution Table to find the t-value for a 95% confidence level with n-1 degrees of freedom (where n is the sample size).
5. Use the following formula to calculate the confidence interval:
\[
\text{Confidence Interval} = \bar{x} \pm \left(t_{\alpha/2} \times \frac{s}{\sqrt{n}}\right)
\]
where:
- \(\bar{x}\) is the sample mean,
- \(t_{\alpha/2}\) is the t-value for the desired confidence level,
- \(s\) is the sample standard deviation,
- \(n\) is the sample size.
Using these steps and the provided data, you can calculate and find the confidence interval.
**Graphical Representation:**
There is a rectangular table included in the image to record the calculated confidence interval.
**Table:**
| Confidence Interval for the Population Mean is between | [ ] | and | [ ] |
This is where your calculated lower and upper limits of the confidence interval should be written after performing the above calculations.
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