Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 11.8 6.3 8.1 6.5 7.9 6.8 7.4 7.3 7.2 9.7 6.8 7.7 9.0 7.8 10.7 8.0 11.6 7.7 7.0 5.9 9.7 8.7 6.3 8.7 7.3 11.3 7.0 (a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: Ex, = 220.2.] (Round your answer to three decimal places.) MPa State which estimator you used. Os Ox Ox Os/x Op (b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%. MPa State which estimator you used. Ox Os/x Os Op 07 (c) Calculate a point estimate of the population standard deviation o. [Hint: Ex2 = 1868.08.] (Round your answer to three decimal places.) MPa Interpret this point estimate. O This estimate describes the bias of the data. O This estimate describes the center of the data. O This estimate describes the spread of the data. O This estimate describes the linearity of the data.
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 11.8 6.3 8.1 6.5 7.9 6.8 7.4 7.3 7.2 9.7 6.8 7.7 9.0 7.8 10.7 8.0 11.6 7.7 7.0 5.9 9.7 8.7 6.3 8.7 7.3 11.3 7.0 (a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: Ex, = 220.2.] (Round your answer to three decimal places.) MPa State which estimator you used. Os Ox Ox Os/x Op (b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%. MPa State which estimator you used. Ox Os/x Os Op 07 (c) Calculate a point estimate of the population standard deviation o. [Hint: Ex2 = 1868.08.] (Round your answer to three decimal places.) MPa Interpret this point estimate. O This estimate describes the bias of the data. O This estimate describes the center of the data. O This estimate describes the spread of the data. O This estimate describes the linearity of the data.
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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![### Example Problem on Point Estimation of Flexural Strength
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
```
11.8 6.3 8.1 6.5 7.9 6.8 7.4
7.3 7.2 9.7 6.8 7.9 9.0 7.8
10.7 8.0 11.6 7.7 7.0 5.9 9.7
8.7 6.3 8.7 7.3 11.3 7.3 7.0
```
#### (a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion.
\[ \bar{x} = \text{MPa} \]
**Hint:** \(\sum x_i = 220.2\). Round your answer to three decimal places.
**State which estimator you used.**
- \( \bigcirc \) \( s \)
- \( \bigcirc \) \( \bar{x} \)
- \( \bigcirc \) \( \tilde{x} \)
- \( \bigcirc \) \( s / \bar{x} \)
- \( \bigcirc \) \( p̂ \)
#### (b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%.
\[ \tilde{x} = \text{MPa} \]
**State which estimator you used.**
- \( \bigcirc \) \( \bar{x} \)
- \( \bigcirc \) \( s / \bar{x} \)
- \( \bigcirc \) \( s \)
- \( \bigcirc \) \( p̂ \)
- \( \bigcirc \) \( \tilde{x} \)
#### (c) Calculate a point estimate of the population standard deviation \( \sigma \).
\[ \sigma = \text{MPa} \]
**Hint:** \(\sum x_i^2 = 1868.08\). Round your answer to three decimal places.
**Interpret this point estimate.**
- \( \bigcirc](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feeb0cd63-fcaf-4f78-a653-01ec8225914a%2Fe0f8052d-affe-4c99-b564-73f6f5440817%2Fzrdud2_processed.png&w=3840&q=75)
Transcribed Image Text:### Example Problem on Point Estimation of Flexural Strength
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
```
11.8 6.3 8.1 6.5 7.9 6.8 7.4
7.3 7.2 9.7 6.8 7.9 9.0 7.8
10.7 8.0 11.6 7.7 7.0 5.9 9.7
8.7 6.3 8.7 7.3 11.3 7.3 7.0
```
#### (a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion.
\[ \bar{x} = \text{MPa} \]
**Hint:** \(\sum x_i = 220.2\). Round your answer to three decimal places.
**State which estimator you used.**
- \( \bigcirc \) \( s \)
- \( \bigcirc \) \( \bar{x} \)
- \( \bigcirc \) \( \tilde{x} \)
- \( \bigcirc \) \( s / \bar{x} \)
- \( \bigcirc \) \( p̂ \)
#### (b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%.
\[ \tilde{x} = \text{MPa} \]
**State which estimator you used.**
- \( \bigcirc \) \( \bar{x} \)
- \( \bigcirc \) \( s / \bar{x} \)
- \( \bigcirc \) \( s \)
- \( \bigcirc \) \( p̂ \)
- \( \bigcirc \) \( \tilde{x} \)
#### (c) Calculate a point estimate of the population standard deviation \( \sigma \).
\[ \sigma = \text{MPa} \]
**Hint:** \(\sum x_i^2 = 1868.08\). Round your answer to three decimal places.
**Interpret this point estimate.**
- \( \bigcirc
![### Statistical Estimation Problems
#### (c) Calculate a Point Estimate of the Population Standard Deviation (σ)
**[Hint: Σx<sub>i</sub><sup>2</sup> = 1868.08.]**
*Round your answer to three decimal places.*
---
\<Input Box\> MPa
### Interpret this Point Estimate
- [ ] This estimate describes the bias of the data.
- [ ] This estimate describes the center of the data.
- [ ] This estimate describes the spread of the data.
- [ ] This estimate describes the linearity of the data.
### Which Estimator Did You Use?
- [ ] \( \hat{p} \)
- [ ] \( \bar{x} \)
- [ ] \( \tilde{x} \)
- [ ] \( s / \bar{x} \)
- [ ] \( s \)
#### (d) Calculate a Point Estimate of the Proportion of Beams Whose Flexural Strength Exceeds 10 MPa
**[Hint: Think of an observation as a "success" if it exceeds 10.]**
*Round your answer to three decimal places.*
---
\<Input Box\>
#### (e) Calculate a Point Estimate of the Population Coefficient of Variation (σ/μ)
*Round your answer to four decimal places.*
---
\<Input Box\>
### State Which Estimator You Used
- [ ] \( \hat{p} \)
- [ ] \( \bar{x} \)
- [ ] \( s \)
- [ ] \( s / \bar{x} \)
- [ ] \( p̂ \)
---
This transcription provides a clear and structured presentation of the estimation questions and corresponding options. Users are prompted to calculate point estimates and interpret them based on given hints and instructions. The format includes space for responses and selections, offering a straightforward and educational approach to statistical estimation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feeb0cd63-fcaf-4f78-a653-01ec8225914a%2Fe0f8052d-affe-4c99-b564-73f6f5440817%2Fo2djes_processed.png&w=3840&q=75)
Transcribed Image Text:### Statistical Estimation Problems
#### (c) Calculate a Point Estimate of the Population Standard Deviation (σ)
**[Hint: Σx<sub>i</sub><sup>2</sup> = 1868.08.]**
*Round your answer to three decimal places.*
---
\<Input Box\> MPa
### Interpret this Point Estimate
- [ ] This estimate describes the bias of the data.
- [ ] This estimate describes the center of the data.
- [ ] This estimate describes the spread of the data.
- [ ] This estimate describes the linearity of the data.
### Which Estimator Did You Use?
- [ ] \( \hat{p} \)
- [ ] \( \bar{x} \)
- [ ] \( \tilde{x} \)
- [ ] \( s / \bar{x} \)
- [ ] \( s \)
#### (d) Calculate a Point Estimate of the Proportion of Beams Whose Flexural Strength Exceeds 10 MPa
**[Hint: Think of an observation as a "success" if it exceeds 10.]**
*Round your answer to three decimal places.*
---
\<Input Box\>
#### (e) Calculate a Point Estimate of the Population Coefficient of Variation (σ/μ)
*Round your answer to four decimal places.*
---
\<Input Box\>
### State Which Estimator You Used
- [ ] \( \hat{p} \)
- [ ] \( \bar{x} \)
- [ ] \( s \)
- [ ] \( s / \bar{x} \)
- [ ] \( p̂ \)
---
This transcription provides a clear and structured presentation of the estimation questions and corresponding options. Users are prompted to calculate point estimates and interpret them based on given hints and instructions. The format includes space for responses and selections, offering a straightforward and educational approach to statistical estimation.
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