https://file.aiquickdraw.com/mathbot/file/172845879491703c1zgtw.jpg

The problem presented asks to test the hypothesis of independence between household size and opinion on prohibiting smoking in public places, based on the contingency table provided. It also specifies using a significance level of \(\alpha = 0.10\) and requires calculating the P-value using a TI-84 Plus calculator. Here’s how we would approach the steps:

### Part (a) State the null and alternative hypotheses:

1. **Null Hypothesis (\(H_0\))**: Household size and opinion on prohibiting smoking in public places are independent.
2. **Alternative Hypothesis (\(H_1\))**: Household size and opinion on prohibiting smoking in public places are not independent.

The appropriate selections for the dropdown menus are:

- \(H_0\): Household size and opinion **are** independent.
- \(H_1\): Household size and opinion **are not** independent.

---

Would you like a breakdown of how to calculate the test statistic and P-value using the data provided? If so, I can walk you through the steps or provide the calculation directly.

### Five follow-up questions:
1. How do you calculate the expected frequencies in a contingency table?
2. What is the test statistic for the chi-square test of independence?
3. How do you interpret the P-value in hypothesis testing?
4. What does a significance level of 0.10 mean in terms of making a decision?
5. How would the conclusion change if the P-value was very close to 0.10?

### Tip:
Always double-check the assumptions of a chi-square test: the sample size should be large enough, and expected counts in each cell should be at least 5 for the test to be valid.

Test the hypothesis of independence between household size and opinion on prohibiting smoking in public places using a significance level of 0.10 and a chi-square test.

Learn how to perform a chi-square test of independence to determine whether household size and opinion on prohibiting smoking in public places are related, based on survey data. This step-by-step guide covers the contingency table analysis and interpretation of P-values with a significance level of 0.10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation