### Example of Paired Data Analysis#### Problem StatementProvide an appropriate response.Data sets A and B are dependent. Find $\overline{d}$.``` A: 6.1 7.1 9.0 6.0 6.1 B: 8.5 7.4 7.3 7.2 8.6```Assume that the paired data came from a population that is normally distributed.#### Choices```O 0.89O -0.94O 0.58O -0.76```### Solution1. **Calculate the differences ($d$) for each pair**: ``` d = A - B For each pair: (6.1 - 8.5) = -2.4 (7.1 - 7.4) = -0.3 (9.0 - 7.3) = 1.7 (6.0 - 7.2) = -1.2 (6.1 - 8.6) = -2.5 ```2. **Find the mean of these differences**: ``` $\overline{d}$ = $\frac{\sum d}{n}$ = $\frac{-2.4 + (-0.3) + 1.7 + (-1.2) + (-2.5)}{5}$ = $\frac{-4.7}{5}$ = -0.94 ```### Explanation- The task is to find the mean difference between two sets of dependent data.- Data set A: 6.1, 7.1, 9.0, 6.0, 6.1- Data set B: 8.5, 7.4, 7.3, 7.2, 8.6- The differences are calculated for each pair, and then the mean of these differences is found.Thus, the correct answer is $-0.94$.

Given information- We have given data sets A and B are dependent. The calculation for mean is shown…

Provide an appropriate response. Data sets A and B are dependent. Find a. 6.1 7.1 9.0 6.0 6.1 B 8.5 7.4 7.3 7.2 8.6 Assume that the paired data came from a population that is normally distributed. O 0.89 O -0.94 O 0.58 -0.76

Provide an appropriate response. Data sets A and B are dependent. Find a. 6.1 7.1 9.0 6.0 6.1 B 8.5 7.4 7.3 7.2 8.6 Assume that the paired data came from a population that is normally distributed. O 0.89 O -0.94 O 0.58 -0.76

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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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

### Example of Paired Data Analysis

#### Problem Statement

Provide an appropriate response.

Data sets A and B are dependent. Find $\overline{d}$.

```
A: 6.1 7.1 9.0 6.0 6.1
B: 8.5 7.4 7.3 7.2 8.6
```

Assume that the paired data came from a population that is normally distributed.

#### Choices

```
O 0.89
O -0.94
O 0.58
O -0.76
```

### Solution

1. **Calculate the differences ($d$) for each pair**:
```
d = A - B
For each pair:
(6.1 - 8.5) = -2.4
(7.1 - 7.4) = -0.3
(9.0 - 7.3) = 1.7
(6.0 - 7.2) = -1.2
(6.1 - 8.6) = -2.5
```

2. **Find the mean of these differences**:
```
$\overline{d}$ = $\frac{\sum d}{n}$
= $\frac{-2.4 + (-0.3) + 1.7 + (-1.2) + (-2.5)}{5}$
= $\frac{-4.7}{5}$
= -0.94
```

### Explanation

- The task is to find the mean difference between two sets of dependent data.
- Data set A: 6.1, 7.1, 9.0, 6.0, 6.1
- Data set B: 8.5, 7.4, 7.3, 7.2, 8.6
- The differences are calculated for each pair, and then the mean of these differences is found.

Thus, the correct answer is $-0.94$.

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