# OpenStax_CNX

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# The Chi-Square Distribution: Practice 2

Summary: Note: This module is currently under revision, and its content is subject to change. This module is being prepared as part of a statistics textbook that will be available for the Fall 2008 semester.

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## Student Learning Outcome

The student will explore the properties of contingency tables.

 smoking level/day ethnicity African American Native Hawaiian Latino Japanese Americans White TOTALS 1-10 11-20 21-30 31+ TOTALS

## Hypothesis Test

Conduct a hypothesis test to determine if smoking level and ethnicity are independent.

## Data

Copy the data from Chapter 3, Practice 2, into the above table.

## Hypothesis

State the hypotheses.

HO:HO: size 12{H rSub { size 8{O} } :} {} ____________________

Ha:Ha: size 12{H rSub { size 8{a} } :} {} ____________________

## Expected Values

Enter expected values on the above table. (Round to two decimal places.)

## Information

Fill in the information below.

### Exercise 1

degrees of freedom = __________

12

### Exercise 2

Chi2Chi2 size 12{ ital "Chi" rSup { size 8{2} } } {} test statistic = __________

10301.8

### Exercise 3

pp size 12{p - {}} {}value = __________

0

### Exercise 4

Is this a right-tailed, left-tailed, or two-tailed test? __________ Explain why.

right

### Exercise 5

Graph the situation. Label and scale the horizontal axis. Mark the mean and test statistic. Shade in the region corresponding to the pp size 12{p - {}} {}value.

## Reason and Conclusion

State the decision and conclusion (in a complete sentence) for the following preconceived levels of αα size 12{α} {} .

### Exercise 6

α = 0 . 05 α = 0 . 05 size 12{α=0 "." "05"} {}

Decision: _____________________________________________________

Reason for the Decision: _________________________________________

Conclusion (write out in a complete sentence): _______________________ __________________________________________________________ __________________________________________________________

#### Solution

Reject the null hypothesis

### Exercise 7

α = 0 . 01 α = 0 . 01 size 12{α=0 "." "01"} {}

Decision: _____________________________________________________

Reason for the Decision: _________________________________________

Conclusion (write out in a complete sentence): _______________________ __________________________________________________________ __________________________________________________________

#### Solution

Reject the null hypothesis

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