MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F. A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population of x values has an approximately normal distribution .
| 85 | 70 | 115 | 80 | 90 | 95 | 30 | 23 | 100 | 110 |
| 105 | 95 | 105 | 60 | 110 | 120 | 95 | 90 | 60 | 70 |
![## Determining the Cost of a Sleeping Bag for Cold Temperatures
When planning an outdoor adventure, it's crucial to have the right sleeping bag. Let’s say you need a sleeping bag that can keep you warm in temperatures ranging from 20°F to 45°F. Below is a random sample of sleeping bag prices (in dollars) suitable for such conditions:
### Sample Prices ($)
```
85, 70, 115, 80, 90, 95, 30, 23, 100, 110
105, 95, 105, 60, 110, 120, 95, 90, 60, 70
```
### Instructions:
#### (a) Calculating Sample Mean Price (\(\bar{x}\)) and Sample Standard Deviation (s)
Use a calculator with mean and sample standard deviation functions to find the following:
- Sample Mean Price (\(\bar{x}\))
- Sample Standard Deviation (s)
*Note: Round your answers to four decimal places.*
\[
\bar{x} = \$ 85.4 \quad \textcolor{green}{✓}
\]
\[
s = \$ 26.5 \quad \textcolor{red}{✗}
\]
#### (b) Finding a Confidence Interval for the Mean Price (\(\mu\))
Using the provided data, treat it as representative of all summer sleeping bag prices. Calculate a 90% confidence interval for the mean price (\(\mu\)) of all summer sleeping bags.
*Note: Round your answers to two decimal places.*
- Lower Limit: `_________`
- Upper Limit: `_________`
### Assistance:
If you need help with the calculations or concepts, refer to the following resources:
- **Read It:** [Link to detailed explanation and examples]
- **Master It:** [Link to practice problems and additional resources]
This guide helps ensure you can budget appropriately for your gear, ensuring both comfort and safety during your outdoor adventures.](https://content.bartleby.com/qna-images/question/fe76f06b-a6e5-4577-ae94-392ea27c231a/3582a82e-339f-41e8-a306-2e504a430c4f/7h3pl7_processed.jpeg)
Transcribed Image Text:## Determining the Cost of a Sleeping Bag for Cold Temperatures
When planning an outdoor adventure, it's crucial to have the right sleeping bag. Let’s say you need a sleeping bag that can keep you warm in temperatures ranging from 20°F to 45°F. Below is a random sample of sleeping bag prices (in dollars) suitable for such conditions:
### Sample Prices ($)
```
85, 70, 115, 80, 90, 95, 30, 23, 100, 110
105, 95, 105, 60, 110, 120, 95, 90, 60, 70
```
### Instructions:
#### (a) Calculating Sample Mean Price (\(\bar{x}\)) and Sample Standard Deviation (s)
Use a calculator with mean and sample standard deviation functions to find the following:
- Sample Mean Price (\(\bar{x}\))
- Sample Standard Deviation (s)
*Note: Round your answers to four decimal places.*
\[
\bar{x} = \$ 85.4 \quad \textcolor{green}{✓}
\]
\[
s = \$ 26.5 \quad \textcolor{red}{✗}
\]
#### (b) Finding a Confidence Interval for the Mean Price (\(\mu\))
Using the provided data, treat it as representative of all summer sleeping bag prices. Calculate a 90% confidence interval for the mean price (\(\mu\)) of all summer sleeping bags.
*Note: Round your answers to two decimal places.*
- Lower Limit: `_________`
- Upper Limit: `_________`
### Assistance:
If you need help with the calculations or concepts, refer to the following resources:
- **Read It:** [Link to detailed explanation and examples]
- **Master It:** [Link to practice problems and additional resources]
This guide helps ensure you can budget appropriately for your gear, ensuring both comfort and safety during your outdoor adventures.
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