https://file.aiquickdraw.com/mathbot/file/17280318102701r0fwn7t.jpg

In the image, you are working on a Chi-square test problem related to seat belt use and smoking habits. The question asks you to define the null and alternative hypotheses and then choose the correct pair of hypotheses based on a study about smokers and seat belt use.

### Here's a breakdown:

1. **Null Hypothesis (\(H_0\))**: 
   This represents the claim that there is no relationship between two variables. In this case, the null hypothesis would suggest that smoking habits are **independent** of seat belt use, meaning smokers and non-smokers are equally likely to wear seat belts.

2. **Alternative Hypothesis (\(H_1\))**: 
   This is the claim that there is a relationship between the two variables. Here, it would suggest that smoking habits **affect** seat belt use, meaning smokers are less likely to wear seat belts compared to non-smokers.

The problem is asking for the correct hypothesis pair to test whether **smoking influences seat belt use**. Given the options:

- **Option B** seems to correctly define the hypotheses:
  - \( H_0 \): The amount of smoking is independent of seat belt use.
  - \( H_1 \): The amount of smoking is not independent of seat belt use.

This is consistent with a Chi-square test, where you check if two categorical variables (smoking and seat belt use) are related or not.

### Do you want any details or have further questions?

#### 5 Related Questions:
1. How do you perform a Chi-square test to evaluate categorical data?
2. What is the significance of the p-value in hypothesis testing?
3. How do you calculate the expected frequencies in a Chi-square test?
4. What are some common assumptions made in Chi-square tests?
5. How does sample size affect the outcome of a Chi-square test?

#### Tip:
In hypothesis testing, always define the null hypothesis as a statement of "no effect" or "no relationship" between the variables being studied.

A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the accompanying table. Use a 0.05 significance level to test the claim that the amount of smoking is independent of seat belt use. A plausible theory is that people who smoke are less concerned about their health and safety and are therefore less inclined to wear seat belts. Define the null and alternative hypotheses.

Test the relationship between smoking habits and seat belt use using a Chi-square test with a 0.05 significance level. The problem involves hypothesis testing and determining whether smoking is independent of seat belt use. Suitable for undergraduate statistics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation