In a survey of 2998 adults, a poll asked people whether they smoked cigarettes and whether they always wear a seat belt in a car. The table shows the results of the survey. For each activity, define success as finding an individual that participates in the hazardous activity. Complete parts (a) and (b).### Table of Survey Results:| | No Seat Belt (success) | Seat Belt (failure) ||-------------------|------------------------|---------------------|| **Smoke (success)** | 54 | 433 || **Do not smoke (failure)** | 346 | 2165 |#### (a) Why is this a dependent sample?- ✅ **A**. The same person answered both questions.- **B**. More than 5% of the population was surveyed.- **C**. The answer to the second question depends on the answer to the first question.- **D**. Two questions were asked.#### (b) Is there a significant difference in the proportion of individuals who smoke and the proportion of individuals that do not wear a seat belt? In other words, is there a significant difference between the proportion of individuals who engage in hazardous activities? Use the α = 0.05 level of significance. Let $ p_1 $ represent the proportion of individuals who smoke and $ p_2 $ represent the proportion of individuals that do not wear a seat belt.**What are the hypotheses for this test?**- ✅ **A**. $ H_0 $: $ p_1 = p_2 $ $ H_1 $: $ p_1 \neq p_2 $- **B**. $ H_0 $: $ p_1 < p_2 $ $ H_1 $: $ p_1 = p_2 $- **C**. $ H_0 $: $ p_1 \neq p_2 $ $ H_1 $: $ p_1 = p_2 $- **D**. $ H_0 $: $ p_1 = p_2 $ $ H_1 $: $ p_1 < p_2 $**Calculate the test statistic.**\[ \chi^2_0 = \] \_\_\_\_\_\_ (Round to two decimal places as needed.)#### Explanation of Graph/ Diagrams ### Chi-Square Distribution Area to the Right#### Table: Chi-Square ($\chi^2$) Distribution Area to the Right of Critical ValueThis chi-square distribution table provides the critical values ($\chi^2$) for different significance levels (0.995, 0.99, 0.975, 0.95, 0.90, 0.10, 0.05, 0.025, 0.01, 0.005) against varying degrees of freedom (df). The chi-square distribution is essential for various statistical analyses, especially for tests involving categorical data.**Explanation of the Table:**- **Degrees of Freedom (df)**: Represented in the first column. It is a parameter that allows us to specify different distributions.- **Significance Levels**: Represented in the top row across various columns. These levels (0.995, 0.99, 0.975, 0.95, 0.90, 0.10, 0.05, 0.025, 0.01, 0.005) indicate the probability of observing a test statistic as extreme as, or more extreme than, the value given (critical value).Each cell in the table represents the critical value ($\chi^2$) for the corresponding degree of freedom and significance level. For example:- For 1 degree of freedom and significance level 0.05, the critical value is 3.841.- For 10 degrees of freedom and significance level 0.01, the critical value is 18.307.Below is the complete chi-square distribution table:| Degrees of Freedom | 0.995 | 0.99 | 0.975 | 0.95 | 0.90 | 0.10 | 0.05 | 0.025 | 0.01 | 0.005 ||--------------------|--------|--------|-------|-------|-------|-------|-------|-------|-------|--------|| 1 | 0.000 | 0.000 | 0.001 | 0.004 | 0.016 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 || 2 | 0.010 | 0

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The chi square test is used to calculate the association between the two variable. The chi sqaure is…

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(failure) Click the icon to view the Chi-square distribution table. (a) Why is this a dependent sample? A. The same person answered both questions. O B. More than 5% of the population was surveyed. O C. The answer to the second question depends on the answer to the first question. O D. Two questions were asked. (b) Is there a significant difference in the proportion of individuals who smoke and the proportion of individuals that do not wear a seat belt? In other words, is there a significant difference between the proportion of individuals who engage in hazardous activities? Use the a = 0.05 level of significance. Let p, represent the proportion of individuals who smoke and p2 represent the proportion of individuals that do not wear a seat belt. What are the hypotheses for this test? VA. Họ: P1 "P2 O B. Ho: P1

(failure) Click the icon to view the Chi-square distribution table. (a) Why is this a dependent sample? A. The same person answered both questions. O B. More than 5% of the population was surveyed. O C. The answer to the second question depends on the answer to the first question. O D. Two questions were asked. (b) Is there a significant difference in the proportion of individuals who smoke and the proportion of individuals that do not wear a seat belt? In other words, is there a significant difference between the proportion of individuals who engage in hazardous activities? Use the a = 0.05 level of significance. Let p, represent the proportion of individuals who smoke and p2 represent the proportion of individuals that do not wear a seat belt. What are the hypotheses for this test? VA. Họ: P1 "P2 O B. Ho: P1

MATLAB: An Introduction with Applications

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Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Question

In a survey of 2998 adults, a poll asked people whether they smoked cigarettes and whether they always wear a seat belt in a car. The table shows the results of the survey. For each activity, define success as finding an individual that participates in the hazardous activity. Complete parts (a) and (b).

### Table of Survey Results:
| | No Seat Belt (success) | Seat Belt (failure) |
|-------------------|------------------------|---------------------|
| **Smoke (success)** | 54 | 433 |
| **Do not smoke (failure)** | 346 | 2165 |

#### (a) Why is this a dependent sample?
- ✅ **A**. The same person answered both questions.
- **B**. More than 5% of the population was surveyed.
- **C**. The answer to the second question depends on the answer to the first question.
- **D**. Two questions were asked.

#### (b) Is there a significant difference in the proportion of individuals who smoke and the proportion of individuals that do not wear a seat belt? In other words, is there a significant difference between the proportion of individuals who engage in hazardous activities? Use the α = 0.05 level of significance. Let $ p_1 $ represent the proportion of individuals who smoke and $ p_2 $ represent the proportion of individuals that do not wear a seat belt.

**What are the hypotheses for this test?**
- ✅ **A**. $ H_0 $: $ p_1 = p_2 $
$ H_1 $: $ p_1 \neq p_2 $
- **B**. $ H_0 $: $ p_1 < p_2 $
$ H_1 $: $ p_1 = p_2 $
- **C**. $ H_0 $: $ p_1 \neq p_2 $
$ H_1 $: $ p_1 = p_2 $
- **D**. $ H_0 $: $ p_1 = p_2 $
$ H_1 $: $ p_1 < p_2 $

**Calculate the test statistic.**
\[ \chi^2_0 = \] \_\_\_\_\_\_ (Round to two decimal places as needed.)

#### Explanation of Graph/ Diagrams

### Chi-Square Distribution Area to the Right

#### Table: Chi-Square ($\chi^2$) Distribution Area to the Right of Critical Value

This chi-square distribution table provides the critical values ($\chi^2$) for different significance levels (0.995, 0.99, 0.975, 0.95, 0.90, 0.10, 0.05, 0.025, 0.01, 0.005) against varying degrees of freedom (df). The chi-square distribution is essential for various statistical analyses, especially for tests involving categorical data.

**Explanation of the Table:**

- **Degrees of Freedom (df)**: Represented in the first column. It is a parameter that allows us to specify different distributions.
- **Significance Levels**: Represented in the top row across various columns. These levels (0.995, 0.99, 0.975, 0.95, 0.90, 0.10, 0.05, 0.025, 0.01, 0.005) indicate the probability of observing a test statistic as extreme as, or more extreme than, the value given (critical value).

Each cell in the table represents the critical value ($\chi^2$) for the corresponding degree of freedom and significance level. For example:
- For 1 degree of freedom and significance level 0.05, the critical value is 3.841.
- For 10 degrees of freedom and significance level 0.01, the critical value is 18.307.

Below is the complete chi-square distribution table:

| Degrees of Freedom | 0.995 | 0.99 | 0.975 | 0.95 | 0.90 | 0.10 | 0.05 | 0.025 | 0.01 | 0.005 |
|--------------------|--------|--------|-------|-------|-------|-------|-------|-------|-------|--------|
| 1 | 0.000 | 0.000 | 0.001 | 0.004 | 0.016 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 |
| 2 | 0.010 | 0

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