https://file.aiquickdraw.com/mathbot/file/1729934361701zdyqz6ox.csv

A random sample of 116 married or de facto couples in the Sydney region has been selected to study non-verbal communication. An experiment was conducted requiring the subject to guess words shown to the partner, without any verbal communication. Some of the variables recorded for each couple are listed below.

Variable		Description
subid		Subject ID
sex		sex of guesser
years		the length of the relationship (in years)
percentage		the percentage of correct guesses
employment		employment status
Research question 1: we are interested in studying the association between the employment status and the sex of guessers in the population under consideration. Report the number of the degrees of freedom [integer]:	Answer 1 Question 1


The dataset contains 116 rows and multiple columns, some of which are unrelated or have null values, such as the columns labeled "Unnamed." The relevant columns for addressing Research Question 1, which concerns the association between *employment status* and *sex* of the guessers, are:

- `sex`: indicating the gender of the guesser
- `employment`: representing employment status

### Calculating Degrees of Freedom

To determine the degrees of freedom for the chi-squared test, we will use the formula:

\[
\text{Degrees of Freedom} = (\text{rows} - 1) \times (\text{columns} - 1)
\]

Let's proceed with analyzing the contingency table between `sex` and `employment` to find these values.The contingency table between employment status and the sex of guessers is as follows:

| Employment  | Casual | Full-time | Part-time | Unemployed |
|-------------|--------|-----------|-----------|------------|
| Female      | 12     | 18        | 22        | 13         |
| Male        | 14     | 9         | 13        | 15         |

Using this table, the degrees of freedom are:

\[
\text{Degrees of Freedom} = (2 - 1) \times (4 - 1) = 3
\]

**Answer to Question 1:** The degrees of freedom is **3**.

Would you like further details on how this table was derived or more context on chi-squared tests?

---

1. What does a chi-squared test reveal about associations between categorical variables?
2. How is the significance level chosen for chi-squared tests in hypothesis testing?
3. What alternative tests could be used if the sample size were smaller?
4. How can we interpret the results of a chi-squared test in this context?
5. What other variables in the dataset could be explored for similar associations?

**Tip:** When calculating degrees of freedom for a contingency table, remember that it's based on the count of unique categories in each variable.

A random sample of 116 married or de facto couples in the Sydney region has been selected to study non-verbal communication. An experiment was conducted requiring the subject to guess words shown to the partner, without any verbal communication. We are interested in studying the association between the employment status and the sex of guessers. Report the number of degrees of freedom.

Explore the association between employment status and the sex of guessers in a study of non-verbal communication among couples in Sydney. Learn to calculate degrees of freedom for a chi-squared test based on a sample size of 116 couples.

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