A researcher wants to study the relationship between salary and gender. She randomly selects 350 individuals and determines their salary and gender. Can the researcher conclude that salary and gender are dependent? Income	Male	Female	Total

Below 25,000-50,000-75,000	24	19	43

Total	170	180	350 State the null and alternative hypothesis.

In this study, the researcher wants to determine whether there is a **relationship (dependency)** between **salary** and **gender**. To do this, we perform a **chi-square test of independence**. Let's begin by formulating the null and alternative hypotheses.

### 1. **Null Hypothesis (H₀):**
- The **null hypothesis** states that there is **no relationship** between salary and gender, meaning that **salary and gender are independent**.
  
  \[
  H_0: \text{Salary and gender are independent.}
  \]

### 2. **Alternative Hypothesis (H₁):**
- The **alternative hypothesis** suggests that there **is a relationship** between salary and gender, meaning that **salary and gender are dependent**.
  
  \[
  H_1: \text{Salary and gender are dependent.}
  \]

### Next Steps:
To test these hypotheses, we will use the chi-square test of independence. This involves comparing the observed frequencies of males and females across different salary categories to the expected frequencies under the assumption that salary and gender are independent.

Would you like to go through the steps of calculating the expected frequencies and chi-square value, or do you have any specific questions? 

Here are 5 related questions to extend your understanding:
1. What is the formula for the chi-square test of independence?
2. How are expected frequencies calculated in a chi-square test?
3. What is the critical value of chi-square for this data?
4. How does the p-value help in making a decision on the hypothesis?
5. What assumptions must be met to use the chi-square test of independence?

**Tip:** The larger the chi-square statistic, the stronger the evidence against the null hypothesis, implying a stronger relationship between the variables.

A researcher wants to study the relationship between salary and gender. She randomly selects 350 individuals and determines their salary and gender. Can the researcher conclude that salary and gender are dependent? Income Male Female Total Below 25,000-50,000-75,000 24 19 43 Total 170 180 350 State the null and alternative hypothesis.

Explore how to determine if there is a relationship between salary and gender using a chi-square test of independence. This detailed guide covers the null and alternative hypotheses, the chi-square test statistic formula, and the key statistical concepts. Suitable for high school and college students.

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