# 11.10 Practice 2: contingency tables

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

## Student learning outcomes

• The student will conduct a test for independence using 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 1: Contingency Tables into the table below.

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.

• ${H}_{o}:$
• ${H}_{a}:$

## Expected values

Enter expected values in the above below. Round to two decimal places.

## Analyze the data

Calculate the following values:

Degrees of freedom =

12

${\text{Chi}}^{2}$ test statistic =

10301.8

p-value =

0

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

right

## Graph the data

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 $\alpha$ .

$\alpha =0\text{.}\text{05}$

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

• Reject the null hypothesis

$\alpha =0.01$

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

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