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