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.)

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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.
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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