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The Chi-Square Distribution: Practice 1

Module by: Dr. Barbara Illowsky, Susan Dean

Summary: 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 explore the properties of goodness-of-fit test data.

Given

The following data are real. The cumulative number of AIDS cases reported for Santa Clara County through December 31, 2003, is broken down by ethnicity as follows:

Ethnicity Number of Cases
White 2032
Hispanic 897
African-American 372
Asian, Pacific Islander 168
Native American 20
  Total = 3489

The percentage of each ethnic group in Santa Clara County is as follows:

Ethnicity Percentage of total county population Number expected (round to 2 decimal places)
White 47.79% 1667.39
Hispanic 24.15%  
African-American 3.55%  
Asian, Pacific Islander 24.21%  
Native American 0.29%  
  Total = 100%  

Expected Results

If the ethnicity of AIDS victims followed the ethnicity of the total county population, fill in the expected number of cases per ethnic group.

Goodness-of-Fit Test

Perform a goodness-of-fit test to determine whether the make-up of AIDS cases follows the ethnicity of the general population of Santa Clara County.

Exercise 1

H o : H o : size 12{H rSub { size 8{O} } :μ rSub { size 8{W} } =μ rSub { size 8{ ital "NW"} } } {}

Exercise 2

H a : H a : size 12{H rSub { size 8{a} } :μ rSub { size 8{W} } <> μ rSub { size 8{ ital "NW"} } } {}

Exercise 3

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

Exercise 4

degrees of freedom =

Solution 4

degrees of freedom = 4

Exercise 5

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

Solution 5

951.69

Exercise 6

p-value =

Solution 6

0

Exercise 7

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

9.png

Let α = 0.05 α=0.05

Decision:

Reason for the Decision:

Conclusion (write out in complete sentences):

Discussion Question

Exercise 8

Does it appear that the pattern of AIDS cases in Santa Clara County corresponds to the distribution of ethnic groups in this county? Why or why not?

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