E Click the icon to view a table of prices of new mobile homes. The 99.7% confidence interval is from $ to $. (Round to the nearest dollar as needed.) Prices of new mobile homes Prices ($1000s) of 36 Randomly Selected New Mobile Homes 57.7 62.6 56.6 68.9 59.9 67.2 72.2 56.2 62.8 62.8 54.6 71.8 62.9 66.6 64.3 50.1 67.1 64.8 73.5 55.9 71.6 49.7 52.0 53.3 72.0 77.2 58.7 61.6 62.8 56.7 55.1 76.1 57.1 71.2 63.4 76.8
E Click the icon to view a table of prices of new mobile homes. The 99.7% confidence interval is from $ to $. (Round to the nearest dollar as needed.) Prices of new mobile homes Prices ($1000s) of 36 Randomly Selected New Mobile Homes 57.7 62.6 56.6 68.9 59.9 67.2 72.2 56.2 62.8 62.8 54.6 71.8 62.9 66.6 64.3 50.1 67.1 64.8 73.5 55.9 71.6 49.7 52.0 53.3 72.0 77.2 58.7 61.6 62.8 56.7 55.1 76.1 57.1 71.2 63.4 76.8
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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![**Educational Text on Estimating Confidence Intervals**
A government bureau publishes annual price figures for new mobile homes. A simple random sample of 36 new mobile homes yielded the following prices, in thousands of dollars. Assume that the population standard deviation of all such prices is $7.8 thousand, that is, $7,800. Use the data to obtain a 99.7% confidence interval for the mean price of all new mobile homes.
**Table of Prices for New Mobile Homes:**
The table lists the prices of 36 newly selected mobile homes, measured in thousands of dollars:
- 68.9, 67.2, 59.9, 57.7, 62.6, 62.8, 54.6, 71.8, 62.9
- 66.6, 72.2, 64.3, 56.6, 67.1, 62.8, 55.9, 50.1, 71.6
- 49.7, 56.2, 72.0, 58.7, 64.8, 62.8, 56.7, 52.0, 53.3
- 55.1, 76.1, 77.2, 61.6, 73.5, 57.1, 71.2, 63.4, 76.8
**Confidence Interval Calculation:**
To calculate the 99.7% confidence interval for the mean price of all new mobile homes, apply the following procedure:
1. **Mean Calculation**: Calculate the sample mean (\( \bar{x} \)) from the given data.
2. **Standard Error**: Use the population standard deviation (\( \sigma = \$7,800 \)) to calculate the standard error (\( SE = \frac{\sigma}{\sqrt{n}} \)) where \( n = 36 \).
3. **Confidence Interval Formula**: Apply the formula for the confidence interval:
\[
\bar{x} \pm Z \times SE
\]
where \( Z \) is the Z-score corresponding to the desired level of confidence (99.7%), often found from statistical tables.
4. **Interval Computation**: Compute the interval to determine the range in which the mean price is expected to fall.
**Note](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2b425c8-1e3a-4bc4-9526-e999f44a089d%2F8fa831be-9794-45bb-b338-736bb5648985%2F96am5ov_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Text on Estimating Confidence Intervals**
A government bureau publishes annual price figures for new mobile homes. A simple random sample of 36 new mobile homes yielded the following prices, in thousands of dollars. Assume that the population standard deviation of all such prices is $7.8 thousand, that is, $7,800. Use the data to obtain a 99.7% confidence interval for the mean price of all new mobile homes.
**Table of Prices for New Mobile Homes:**
The table lists the prices of 36 newly selected mobile homes, measured in thousands of dollars:
- 68.9, 67.2, 59.9, 57.7, 62.6, 62.8, 54.6, 71.8, 62.9
- 66.6, 72.2, 64.3, 56.6, 67.1, 62.8, 55.9, 50.1, 71.6
- 49.7, 56.2, 72.0, 58.7, 64.8, 62.8, 56.7, 52.0, 53.3
- 55.1, 76.1, 77.2, 61.6, 73.5, 57.1, 71.2, 63.4, 76.8
**Confidence Interval Calculation:**
To calculate the 99.7% confidence interval for the mean price of all new mobile homes, apply the following procedure:
1. **Mean Calculation**: Calculate the sample mean (\( \bar{x} \)) from the given data.
2. **Standard Error**: Use the population standard deviation (\( \sigma = \$7,800 \)) to calculate the standard error (\( SE = \frac{\sigma}{\sqrt{n}} \)) where \( n = 36 \).
3. **Confidence Interval Formula**: Apply the formula for the confidence interval:
\[
\bar{x} \pm Z \times SE
\]
where \( Z \) is the Z-score corresponding to the desired level of confidence (99.7%), often found from statistical tables.
4. **Interval Computation**: Compute the interval to determine the range in which the mean price is expected to fall.
**Note
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