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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Description: 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

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

Math

Statistics

(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

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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