A chi-squared test of independence is run to answer the research question.
Consider the output of the test below, and answer the questions:

Pearson's Chi-squared test

data:  table(var1, var4)
`X-squared = 1.5685, df = 3, p-value = 0.6665`

What is the null hypothesis? Choose one among the following options:

a. employment status is associated with sex of guesser

b. employment status in the Sydney region is not distributed according to the given table of probabilities

c. employment status and sex of guesser are independent

d. employment status in the Sydney region is distributed according to the given table of probabilities

The correct null hypothesis for this chi-squared test of independence is:

**c. employment status and sex of guesser are independent**

This is because a chi-squared test of independence is used to test whether two categorical variables (in this case, employment status and sex of guesser) are associated or independent of each other. The null hypothesis assumes that there is no association between the two variables (they are independent), while the alternative hypothesis assumes that they are associated.

### Do you need more details or have any questions?

### Related questions:
1. What does the p-value of 0.6665 indicate about the null hypothesis?
2. How do degrees of freedom (df = 3) relate to the structure of the contingency table?
3. What would it mean if the p-value were below 0.05?
4. How does Pearson’s chi-squared statistic (X-squared = 1.5685) affect the interpretation of the results?
5. What assumptions must be met for a chi-squared test to be valid?

### Tip: 
When the p-value is greater than the significance level (commonly 0.05), the null hypothesis is not rejected, implying that the variables are likely independent.

A chi-squared test of independence is run to answer the research question. Consider the output of the test below, and answer the questions:

Pearson's Chi-squared test

data

Explore how to perform a chi-squared test of independence with a sample problem involving employment status and sex of guesser. This example includes the chi-squared statistic, degrees of freedom, and p-value interpretation. Perfect for undergraduate statistics or data science students.

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