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# The Chi-Square Distribution: Practice 2

Summary: This module provides a practice on Chi-Square Distribution as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

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## Student Learning Outcomes

• The student will explore the properties of contingency tables.

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

## Collect the Data

Copy the data provided in Probability Topics Practice 2: Calculating Probabilities into the table below.

Table 1: Smoking Levels by Ethnicity (Observed)
Smoking Level Per Day African American Native Hawaiian Latino Japanese Americans White TOTALS
1-10
11-20
21-30
31+
TOTALS

## 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 in the above below. Round to two decimal places.

## Analyze the Data

Calculate the following values:

### Exercise 1

Degrees of freedom =

12

### Exercise 2

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

10301.8

p-value =

0

### Exercise 4

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

right

## Graph the Data

### Exercise 5

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

## Conclusions

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"} {}

• a. Decision:
• b. Reason for the decision:
• c. Conclusion (write out in a complete sentence):

#### Solution

• a. Reject the null hypothesis

### Exercise 7

α=0.01 α=0.01

• a. Decision:
• b. Reason for the decision:
• c. Conclusion (write out in a complete sentence):

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