I need help with 5. **Buckle Up! ~ How Does Seat Belt Use Vary with Drivers’ Ethnic Group?**It is well known that location and gender (males are less likely to buckle up) are factors. Here is the data and the mosaic plot for a random sample of male drivers observed in Houston.### Table: Ethnic Group of Driver and Seat Belt Use| Ethnic group of driver | Belted | Not Belted | Total ||------------------------|--------|------------|-------|| Black | 273 | 98 | 371 || Hispanic | 380 | 162 | 542 || White | 199 | 67 | 266 || **Total** | **852**| **327** | **1179**|### Mosaic Plot: Seat Belt Use by Ethnic Group#### DescriptionThe mosaic plot below the table visually represents the distribution of seat belt use among different ethnic groups. Here’s what each segment and color represent:- **Ethnic Groups (Horizontal Axis)**: The ethnic groups are displayed along the horizontal axis, ordered as Black, Hispanic, and White.- **Use of Seat Belt (Vertical Sections)**: Each ethnic group is divided into two vertical sections. - **Green Section**: Represents the proportion of drivers wearing a seat belt. - **Blue Section**: Represents the proportion of drivers not wearing a seat belt.**Observations from the Mosaic Plot**:- The Hispanic group shows a higher total number of observations, represented by the widest segment.- For each ethnic group, a larger green section indicates a higher proportion of belted drivers.- The Black and Hispanic groups have a substantial number of drivers wearing seat belts in comparison to those not wearing seat belts.- The White group also has a larger portion of belted drivers, though the overall numbers are smaller compared to the Black and Hispanic groups.The plot effectively highlights the differences in seat belt usage among the observed ethnic groups, with a clear predominance of seat belt usage across all groups. ### Assessing the Relationship Between Seat Belt Use and Ethnic Group: An Educational Guide**1. Select the name of the test that should be used to assess if there is a relationship between seat belt use and ethnic group.**- **$ \chi^2 $ test of independence** - One-proportion z-test- $ \chi^2 $ goodness of fitThe correct answer is: $ \chi^2 $ test of independence**2. Which of the following conditions must be met for the hypothesis test to be valid? Select all that apply.**- [ ] A. The sample size must be at least 30 or the population data must be normally distributed.- [x] B. There must be an expected count of at least 5 in every cell of the table.- [x] C. The observations must be independent of one another.- [ ] D. There must be at least 10 "success" and 10 "failure" observations.The correct answers are: B and C.**3. What is the expected value for the number of Hispanic drivers who were wearing a seat belt?**(Expected value = 391.6743)**4. State the degrees of freedom for this test.**($ df = 2 $)Degrees of freedom ($ df $) is calculated based on the formula:\[ df = (number \ of \ rows - 1) \times (number \ of \ columns - 1) \]**5. Calculate the test statistic.**(Test statistic = 2.440341)**6. What was the contribution toward this test statistic of Hispanic drivers who were wearing a seat belt?**(Test statistic contribution = 0.347713)**7. Calculate the p-value for this test.**(p = 0.29518)**8. Based on the above p-value, we have _____ evidence against the null hypothesis.**(Based on the p-value, we have **little** evidence against the null hypothesis.)In conclusion, these steps demonstrate how to perform a $ \chi^2 $ test of independence to assess if there is a relationship between two categorical variables—in this context, seat belt use and ethnic group. The degrees of freedom, test statistic, and p-value are essential components in determining the significance of the results derived from the data.

Given, Ethnic group Belted Non Belted Total Black 273 98 371 Hispanic 380 162 542 white…

Vary etnhic group? location and gender (males are le factors. Here is the data and the mosaic plot for a random sample of male drivers observed in Houston. Ethnic group of driver Belted Not Belted Total Black 273 98 371 Hispanic 380 162 542 White 199 67 266 Total 852 327 1179 Ethnicity Black Hispanic White ing a seat belt

Vary etnhic group? location and gender (males are le factors. Here is the data and the mosaic plot for a random sample of male drivers observed in Houston. Ethnic group of driver Belted Not Belted Total Black 273 98 371 Hispanic 380 162 542 White 199 67 266 Total 852 327 1179 Ethnicity Black Hispanic White ing a seat belt

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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Question

I need help with 5.

**Buckle Up! ~ How Does Seat Belt Use Vary with Drivers’ Ethnic Group?**

It is well known that location and gender (males are less likely to buckle up) are factors. Here is the data and the mosaic plot for a random sample of male drivers observed in Houston.

### Table: Ethnic Group of Driver and Seat Belt Use
| Ethnic group of driver | Belted | Not Belted | Total |
|------------------------|--------|------------|-------|
| Black | 273 | 98 | 371 |
| Hispanic | 380 | 162 | 542 |
| White | 199 | 67 | 266 |
| **Total** | **852**| **327** | **1179**|

### Mosaic Plot: Seat Belt Use by Ethnic Group

#### Description

The mosaic plot below the table visually represents the distribution of seat belt use among different ethnic groups. Here’s what each segment and color represent:

- **Ethnic Groups (Horizontal Axis)**: The ethnic groups are displayed along the horizontal axis, ordered as Black, Hispanic, and White.
- **Use of Seat Belt (Vertical Sections)**: Each ethnic group is divided into two vertical sections.
- **Green Section**: Represents the proportion of drivers wearing a seat belt.
- **Blue Section**: Represents the proportion of drivers not wearing a seat belt.

**Observations from the Mosaic Plot**:
- The Hispanic group shows a higher total number of observations, represented by the widest segment.
- For each ethnic group, a larger green section indicates a higher proportion of belted drivers.
- The Black and Hispanic groups have a substantial number of drivers wearing seat belts in comparison to those not wearing seat belts.
- The White group also has a larger portion of belted drivers, though the overall numbers are smaller compared to the Black and Hispanic groups.

The plot effectively highlights the differences in seat belt usage among the observed ethnic groups, with a clear predominance of seat belt usage across all groups.

### Assessing the Relationship Between Seat Belt Use and Ethnic Group: An Educational Guide

**1. Select the name of the test that should be used to assess if there is a relationship between seat belt use and ethnic group.**

- **$ \chi^2 $ test of independence**
- One-proportion z-test
- $ \chi^2 $ goodness of fit

The correct answer is: $ \chi^2 $ test of independence

**2. Which of the following conditions must be met for the hypothesis test to be valid? Select all that apply.**

- [ ] A. The sample size must be at least 30 or the population data must be normally distributed.
- [x] B. There must be an expected count of at least 5 in every cell of the table.
- [x] C. The observations must be independent of one another.
- [ ] D. There must be at least 10 "success" and 10 "failure" observations.

The correct answers are: B and C.

**3. What is the expected value for the number of Hispanic drivers who were wearing a seat belt?**

(Expected value = 391.6743)

**4. State the degrees of freedom for this test.**

($ df = 2 $)

Degrees of freedom ($ df $) is calculated based on the formula:
\[ df = (number \ of \ rows - 1) \times (number \ of \ columns - 1) \]

**5. Calculate the test statistic.**

(Test statistic = 2.440341)

**6. What was the contribution toward this test statistic of Hispanic drivers who were wearing a seat belt?**

(Test statistic contribution = 0.347713)

**7. Calculate the p-value for this test.**

(p = 0.29518)

**8. Based on the above p-value, we have _____ evidence against the null hypothesis.**

(Based on the p-value, we have **little** evidence against the null hypothesis.)

In conclusion, these steps demonstrate how to perform a $ \chi^2 $ test of independence to assess if there is a relationship between two categorical variables—in this context, seat belt use and ethnic group. The degrees of freedom, test statistic, and p-value are essential components in determining the significance of the results derived from the data.

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