Using a quantitative variable of pounds lost in the first year after weight loss surgery, I have created 30 sample data values ranging from 50-113. The mean is 80.23. Based on the formula provided and a 95% confidence interval, the margin of error, E, is 5.75.Do you agree with the margin of error, E, that was calculated? If yes, what is the margin of error and what does it tell you? If not, correct it showing the correct steps.Do you think that it is ever possible to use a sample to estimate a population parameter with 100% accuracy? Explain. ### Weight Loss Data Analysis#### Data Table:The table below represents the pounds lost by individuals over a certain period. This data is organized into two columns.| Lbs. | Lost ||------|------|| 110 | 72 || 82 | 113 || 64 | 94 || 91 | 61 || 104 | 72 || 85 | 83 || 77 | 94 || 50 | 55 || 81 | 64 || 96 | 75 || 74 | 86 || 91 | 97 || 66 | 51 || 80 | 82 || 82 | 75 |#### Statistical Analysis:- **Average (Mean):** The average number of pounds lost is calculated to be **80.23**.- **Standard Deviation:** The standard deviation of the pounds lost is calculated to be **16.06**.---This table can be useful for understanding the distribution and variability of weight loss outcomes in a particular group of individuals. The average provides a central value to the data, while the standard deviation indicates the degree of variation from this average. ### Confidence Interval for Means#### Instructions:Enter Values in the Yellow Boxes Below1. **Sample Size (n):** 302. **Sample Mean (x̄):** 80.23 (be careful with rounding!)3. **Population Standard Deviation (σ):** 16.064. **Confidence Level:** 95% (select from the drop-down menu)5. **Margin of Error (E):** (only enter if given)#### Calculated Values:- **Z critical value:** 1.96- **Margin of Error:** 5.74700- **Minimum Sample Size:** Not Applicable (NA)#### Conclusion:- **Confidence Interval for the Mean:** \( 74.4830028079585 \leq \mu \leq 85.976971920415 \)This interval suggests that we are 95% confident that the true population mean (μ) lies between 74.4830 and 85.9770.

Solution: Let X be the pounds lost. From the given information, x-bar = 80.23, population standard…

Answered: Confidence Interval for MEANS Enter…

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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Using a quantitative variable of pounds lost in the first year after weight loss surgery, I have created 30 sample data values ranging from 50-113. The mean is 80.23. Based on the formula provided and a 95% confidence interval, the margin of error, E, is 5.75.

Do you agree with the margin of error, E, that was calculated? If yes, what is the margin of error and what does it tell you? If not, correct it showing the correct steps.

Do you think that it is ever possible to use a sample to estimate a population parameter with 100% accuracy? Explain.

### Weight Loss Data Analysis

#### Data Table:
The table below represents the pounds lost by individuals over a certain period. This data is organized into two columns.

| Lbs. | Lost |
|------|------|
| 110 | 72 |
| 82 | 113 |
| 64 | 94 |
| 91 | 61 |
| 104 | 72 |
| 85 | 83 |
| 77 | 94 |
| 50 | 55 |
| 81 | 64 |
| 96 | 75 |
| 74 | 86 |
| 91 | 97 |
| 66 | 51 |
| 80 | 82 |
| 82 | 75 |

#### Statistical Analysis:

- **Average (Mean):**
The average number of pounds lost is calculated to be **80.23**.

- **Standard Deviation:**
The standard deviation of the pounds lost is calculated to be **16.06**.

---

This table can be useful for understanding the distribution and variability of weight loss outcomes in a particular group of individuals. The average provides a central value to the data, while the standard deviation indicates the degree of variation from this average.

### Confidence Interval for Means

#### Instructions:
Enter Values in the Yellow Boxes Below

1. **Sample Size (n):** 30
2. **Sample Mean (x̄):** 80.23 (be careful with rounding!)
3. **Population Standard Deviation (σ):** 16.06
4. **Confidence Level:** 95% (select from the drop-down menu)
5. **Margin of Error (E):** (only enter if given)

#### Calculated Values:
- **Z critical value:** 1.96
- **Margin of Error:** 5.74700
- **Minimum Sample Size:** Not Applicable (NA)

#### Conclusion:
- **Confidence Interval for the Mean:**
\( 74.4830028079585 \leq \mu \leq 85.976971920415 \)

This interval suggests that we are 95% confident that the true population mean (μ) lies between 74.4830 and 85.9770.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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