### Analysis of Dissolved Organic Carbon Concentration in Organic Soil Samples The following data represent the concentration of dissolved organic carbon (mg/L) collected from 20 samples of organic soil. Assume that the population is normally distributed. Complete parts (a) through (c) below: #### Data: ``` 7.40 29.80 27.10 16.51 17.50 8.81 15.72 20.46 14.90 33.67 30.91 14.86 15.42 15.35 9.72 19.80 14.86 8.09 20.46 18.30 ``` #### (a) Find the sample mean. The sample mean is ______. (Round to two decimal places as needed.) #### (b) Find the sample standard deviation. The sample standard deviation is ______. (Round to two decimal places as needed.) #### (c) Construct a 98% confidence interval for the population mean μ. The 98% confidence interval for the population mean μ is (______, ______). (Round to two decimal places as needed.) --- For help in calculating the sample mean, sample standard deviation, and constructing confidence intervals, you can use the following formulas: **Sample Mean (x̄):** \[ \bar{x} = \frac{\sum x_i}{n} \] Where \( \sum x_i \) is the sum of all sample values and \( n \) is the number of samples. **Sample Standard Deviation (s):** \[ s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}} \] **Confidence Interval for the Mean:** \[ \bar{x} \pm t_{\alpha/2} \left(\frac{s}{\sqrt{n}}\right) \] Where \( t_{\alpha/2} \) is the t-score corresponding to the desired confidence level (for 98%, use the t-table for the appropriate degrees of freedom), \( s \) is the sample standard deviation, and \( n \) is the sample size.
### Analysis of Dissolved Organic Carbon Concentration in Organic Soil Samples The following data represent the concentration of dissolved organic carbon (mg/L) collected from 20 samples of organic soil. Assume that the population is normally distributed. Complete parts (a) through (c) below: #### Data: ``` 7.40 29.80 27.10 16.51 17.50 8.81 15.72 20.46 14.90 33.67 30.91 14.86 15.42 15.35 9.72 19.80 14.86 8.09 20.46 18.30 ``` #### (a) Find the sample mean. The sample mean is ______. (Round to two decimal places as needed.) #### (b) Find the sample standard deviation. The sample standard deviation is ______. (Round to two decimal places as needed.) #### (c) Construct a 98% confidence interval for the population mean μ. The 98% confidence interval for the population mean μ is (______, ______). (Round to two decimal places as needed.) --- For help in calculating the sample mean, sample standard deviation, and constructing confidence intervals, you can use the following formulas: **Sample Mean (x̄):** \[ \bar{x} = \frac{\sum x_i}{n} \] Where \( \sum x_i \) is the sum of all sample values and \( n \) is the number of samples. **Sample Standard Deviation (s):** \[ s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}} \] **Confidence Interval for the Mean:** \[ \bar{x} \pm t_{\alpha/2} \left(\frac{s}{\sqrt{n}}\right) \] Where \( t_{\alpha/2} \) is the t-score corresponding to the desired confidence level (for 98%, use the t-table for the appropriate degrees of freedom), \( s \) is the sample standard deviation, and \( n \) is the sample size.
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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![### Analysis of Dissolved Organic Carbon Concentration in Organic Soil Samples
The following data represent the concentration of dissolved organic carbon (mg/L) collected from 20 samples of organic soil. Assume that the population is normally distributed. Complete parts (a) through (c) below:
#### Data:
```
7.40 29.80 27.10 16.51 17.50
8.81 15.72 20.46 14.90 33.67
30.91 14.86 15.42 15.35 9.72
19.80 14.86 8.09 20.46 18.30
```
#### (a) Find the sample mean.
The sample mean is ______.
(Round to two decimal places as needed.)
#### (b) Find the sample standard deviation.
The sample standard deviation is ______.
(Round to two decimal places as needed.)
#### (c) Construct a 98% confidence interval for the population mean μ.
The 98% confidence interval for the population mean μ is (______, ______).
(Round to two decimal places as needed.)
---
For help in calculating the sample mean, sample standard deviation, and constructing confidence intervals, you can use the following formulas:
**Sample Mean (x̄):**
\[ \bar{x} = \frac{\sum x_i}{n} \]
Where \( \sum x_i \) is the sum of all sample values and \( n \) is the number of samples.
**Sample Standard Deviation (s):**
\[ s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}} \]
**Confidence Interval for the Mean:**
\[ \bar{x} \pm t_{\alpha/2} \left(\frac{s}{\sqrt{n}}\right) \]
Where \( t_{\alpha/2} \) is the t-score corresponding to the desired confidence level (for 98%, use the t-table for the appropriate degrees of freedom), \( s \) is the sample standard deviation, and \( n \) is the sample size.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff49bfa06-610d-436d-895b-1c7adaa0d334%2F06092d62-fc21-466e-b444-83ce0b4e43b9%2Frmuupnm_processed.png&w=3840&q=75)
Transcribed Image Text:### Analysis of Dissolved Organic Carbon Concentration in Organic Soil Samples
The following data represent the concentration of dissolved organic carbon (mg/L) collected from 20 samples of organic soil. Assume that the population is normally distributed. Complete parts (a) through (c) below:
#### Data:
```
7.40 29.80 27.10 16.51 17.50
8.81 15.72 20.46 14.90 33.67
30.91 14.86 15.42 15.35 9.72
19.80 14.86 8.09 20.46 18.30
```
#### (a) Find the sample mean.
The sample mean is ______.
(Round to two decimal places as needed.)
#### (b) Find the sample standard deviation.
The sample standard deviation is ______.
(Round to two decimal places as needed.)
#### (c) Construct a 98% confidence interval for the population mean μ.
The 98% confidence interval for the population mean μ is (______, ______).
(Round to two decimal places as needed.)
---
For help in calculating the sample mean, sample standard deviation, and constructing confidence intervals, you can use the following formulas:
**Sample Mean (x̄):**
\[ \bar{x} = \frac{\sum x_i}{n} \]
Where \( \sum x_i \) is the sum of all sample values and \( n \) is the number of samples.
**Sample Standard Deviation (s):**
\[ s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}} \]
**Confidence Interval for the Mean:**
\[ \bar{x} \pm t_{\alpha/2} \left(\frac{s}{\sqrt{n}}\right) \]
Where \( t_{\alpha/2} \) is the t-score corresponding to the desired confidence level (for 98%, use the t-table for the appropriate degrees of freedom), \( s \) is the sample standard deviation, and \( n \) is the sample size.
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