Please disregard question 2 in the images. ### Chapter 141. In a manufacturing process, the assembly line speed (feet per minute) was thought to affect the number of defective parts found during the inspection process. To test this theory, managers devised a situation in which the same batch of parts was inspected visually at a variety of line speeds. They collected the following data.| Line Speed (x) | Number of Defective Parts Found (y) ||----------------|-------------------------------------|| 20 | 21 || 20 | 19 || 40 | 15 || 30 | 16 || 60 | 14 || 40 | 17 |### AnalysisIn this study, the line speed is the independent variable (x), and the number of defective parts found is the dependent variable (y). The data presents a variety of line speeds and the corresponding number of defective parts detected during inspection. This data can be used to analyze whether a correlation exists between line speed and defect rate, and if so, how changing the line speed impacts the number of defects. ### Statistical Analysis: Correlation and Significance Testing#### Problem Statement**d.** Compute the sample correlation coefficient between the number of defective parts found and the line speed.**e.** Is the relationship between speed and parts defective significant? Use α = 0.05.The tasks mentioned above focus on calculating the sample correlation coefficient to understand the relationship between two variables: the number of defective parts found and the line speed. Additionally, the significance of this relationship is to be evaluated using a significance level (α) of 0.05.#### Case Study**2.** A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the ...The given case study involves an empirical investigation conducted by a sociologist. The aim is to explore the relationship between two socio-economic factors: - The number of unauthorized days employees are absent per year.- The distance (in miles) between the employees' homes and their workplace.This research aims to determine if there is a correlational relationship between these two variables within the context of a large city hospital.**Visual Representation:**_**Graphs and Diagrams (Explanation):**_Although not provided in the image, typical visual representations for such problems might include:1. **Scatter Plots:** - A scatter plot of defective parts against line speed to visually assess the correlation. - A scatter plot depicting the number of unauthorized absence days against the distance from home to work.2. **Correlation Matrix:** - A matrix to show the correlation coefficients between multiple variables if the data set includes more than the two variables in question.3. **Regression Line:** - A line of best fit on the scatter plots to highlight the trend and assist in assessing the strength and direction of the correlation.4. **Significance Testing Output:** - Results from statistical software indicating the p-value associated with the correlation test to assess significance.**Educational Focus:**- **Understanding Correlation Coefficients:** Learn how to compute and interpret correlation coefficients to assess linear relationships between variables. - **Significance Testing:** Understand how to perform significance testing using α = 0.05 to determine if the observed relationship is statistically significant. - **Impact of Socio-Economic Factors:** Explore how socio-economic variables such as workplace distance and absenteeism

1) Solution: Let x =Line Speed and y = Number of defective parts x y xy x^2 y^2 20 21 420…

Answered: d. Compute the sample correlation…

d. Compute the sample correlation coefficient between the number of defective parts found and the line speed. e. Is the relationship between speed and parts defective significant? Use a = 0.05.

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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Please disregard question 2 in the images.

### Chapter 14

1. In a manufacturing process, the assembly line speed (feet per minute) was thought to affect the number of defective parts found during the inspection process. To test this theory, managers devised a situation in which the same batch of parts was inspected visually at a variety of line speeds. They collected the following data.

| Line Speed (x) | Number of Defective Parts Found (y) |
|----------------|-------------------------------------|
| 20 | 21 |
| 20 | 19 |
| 40 | 15 |
| 30 | 16 |
| 60 | 14 |
| 40 | 17 |

### Analysis
In this study, the line speed is the independent variable (x), and the number of defective parts found is the dependent variable (y). The data presents a variety of line speeds and the corresponding number of defective parts detected during inspection. This data can be used to analyze whether a correlation exists between line speed and defect rate, and if so, how changing the line speed impacts the number of defects.

### Statistical Analysis: Correlation and Significance Testing

#### Problem Statement

**d.** Compute the sample correlation coefficient between the number of defective parts found and the line speed.

**e.** Is the relationship between speed and parts defective significant? Use α = 0.05.

The tasks mentioned above focus on calculating the sample correlation coefficient to understand the relationship between two variables: the number of defective parts found and the line speed. Additionally, the significance of this relationship is to be evaluated using a significance level (α) of 0.05.

#### Case Study

**2.** A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the ...

The given case study involves an empirical investigation conducted by a sociologist. The aim is to explore the relationship between two socio-economic factors:
- The number of unauthorized days employees are absent per year.
- The distance (in miles) between the employees' homes and their workplace.

This research aims to determine if there is a correlational relationship between these two variables within the context of a large city hospital.

**Visual Representation:**

_**Graphs and Diagrams (Explanation):**_

Although not provided in the image, typical visual representations for such problems might include:

1. **Scatter Plots:**
- A scatter plot of defective parts against line speed to visually assess the correlation.
- A scatter plot depicting the number of unauthorized absence days against the distance from home to work.

2. **Correlation Matrix:**
- A matrix to show the correlation coefficients between multiple variables if the data set includes more than the two variables in question.

3. **Regression Line:**
- A line of best fit on the scatter plots to highlight the trend and assist in assessing the strength and direction of the correlation.

4. **Significance Testing Output:**
- Results from statistical software indicating the p-value associated with the correlation test to assess significance.

**Educational Focus:**

- **Understanding Correlation Coefficients:**
Learn how to compute and interpret correlation coefficients to assess linear relationships between variables.

- **Significance Testing:**
Understand how to perform significance testing using α = 0.05 to determine if the observed relationship is statistically significant.

- **Impact of Socio-Economic Factors:**
Explore how socio-economic variables such as workplace distance and absenteeism

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