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The Chi-Square Distribution: Practice 2

Module by: Barbara Illowsky, Ph.D., Susan Dean. E-mail the authors

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.

Note: You are viewing an old version of this document. The latest version is available here.

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 =

Solution

12

Exercise 2

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

Solution

10301.8

Exercise 3

p-value =

Solution

0

Exercise 4

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

Solution

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.

Blank graph with vertical and horizontal axes.

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

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