# Chi-Square - Test of Independence (Worksheet)

- Page ID
- 1386

[ "article:topic", "authorname:openstax" ]

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

*Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.*

### Student Learning Outcome

- The student will evaluate if there is a significant relationship between favorite type of snack and gender.

### Collect the Data

- Using your class as a sample, complete the following chart. Ask each other what your favorite snack is, then total the results.
NOTE: You may need to combine two food categories so that each cell has an expected value of at least five.

Favorite type of snack **sweets (candy & baked goods)****ice cream****chips & pretzels****fruits & vegetables****Total**male female Total - Looking at Table, does it appear to you that there is a dependence between gender and favorite type of snack food? Why or why not?

### Hypothesis Test

Conduct a hypothesis test to determine if the factors are independent:

- \(H_{0}\): ________
- \(H_{a}\): ________
- What distribution should you use for a hypothesis test?
- Why did you choose this distribution?
- Calculate the test statistic.
- Find the
*p*-value. - Sketch a graph of the situation. Label and scale the \(x\)-axis. Shade the area corresponding to the \(p\text{-value}\).
**Figure 11.9.1.** - State your decision.
- State your conclusion in a complete sentence.

### Discussion Questions

- Is the conclusion of your study the same as or different from your answer to answer to question two under Collect the Data?
- Why do you think that occurred?