### Analysis of Smoking Habits and Seat Belt UsageThe following data represent a sample of people's smoking habits and their usage of seat belts while in a car. A researcher aims to determine whether there is a relationship between smoking habits and seat belt usage. The test is conducted at the $\alpha = 0.05$ level of significance.#### Data Table| | No Seat Belt | Seat Belt ||----------------------|--------------|-----------|| **Smoke** | 67 | 448 || **Do not Smoke** | 327 | 2,187 |*Source: Harris Poll*#### Hypothesis Testing Stepsa. **Determine the null and alternative hypotheses.** - $ H_0 $ : Smoking habits and seat belt usage are independent. - $ H_a $ : Smoking habits and seat belt usage are dependent.b. **Determine the test statistic.** Round to two decimal places. \[ \chi^2 = \_\_\_\_ \]c. **Determine the $ p $-value.** Round to four decimal places. \[ p\text{-value} = \_\_\_\_ \]d. **Make a decision.** - $ \bigcirc $ Reject the null hypothesis. - $ \bigcirc $ Fail to reject the null hypothesis.e. **Make a conclusion.** - $ \bigcirc $ There is sufficient evidence to support the claim that smoking habits and seat belt usage are related. ### Hypothesis Testing Example from MyOpenMath**Problem Statement:**You are tasked with determining the relationship between smoking habits and seat belt usage. Follow these steps to hypothesize, calculate, and conclude your findings.---#### a. Determine the null and alternative hypotheses.There are two sets of hypotheses provided. Choose the appropriate one based on the nature of the study. 1. - $ H_0 $: Smoking habits and seat belt usage have the same distribution. - $ H_a $: Smoking habits and seat belt usage follow a different distribution.2. - $ H_0 $: Smoking habits and seat belt usage are independent. - $ H_a $: Smoking habits and seat belt usage are dependent.---#### b. Determine the Test Statistic. Round to two decimal places.\[ \chi^2 = \boxed{\phantom{0.00}} \]---#### c. Determine the $ p $-value. Round to four decimal places.\[ p\text{-value} = \boxed{\phantom{0.0000}} \]---#### d. Make a decision.Choose one of the following based on the calculated test statistic and $ p $-value:- $ \circ $ Reject the null hypothesis.- $ \bullet $ Fail to reject the null hypothesis.---#### e. Make a conclusion.Based on the decision made in part (d), select the correct conclusion:- $ \circ $ There is sufficient evidence to support the claim that smoking habits and seat belt usage are related.- $ \circ $ There is not sufficient evidence to support the claim that smoking habits and seat belt usage are related.---**Note:** This is an educational exercise in hypothesis testing, specifically focusing on the independence of two categorical variables and using the chi-square ($ \chi^2 $) test.

a) Option B is correctb) The chi-square statistic is 0.

Answered: he following data represent a sample of…

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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