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.