11.7 Practice 1: goodness-of-fit test

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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 goodness-of-fit test.

Given

The following data are real. The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as follows:(Source: HIV/AIDS Epidemiology Santa Clara County, Santa Clara County Public Health Department, May 2011 )

Ethnicity Number of Cases
Total = 4075
White 2229
Hispanic 1157
Black/African-American 457
Asian, Pacific Islander 232

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)
Total = 100%
White 42.9% 1748.18
Hispanic 26.7%
Black/African-American 2.6%
Asian, Pacific Islander 27.8%

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.

${H}_{o}:$

${H}_{a}:$

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

degrees of freedom =

degrees of freedom = 3

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

2016.14

p-value =

Rounded to 4 decimal places, the p-value is 0.0000.

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

Let $\alpha =0.05$

Decision:

Reason for the Decision:

Conclusion (write out in complete sentences):

Discussion question

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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Source:  OpenStax, Collaborative statistics (with edits: teegarden). OpenStax CNX. Jul 20, 2009 Download for free at http://legacy.cnx.org/content/col10561/1.3
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