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Chapter 12: Q. 12.98 (page 518)
If a variable of two populations has only two possible values, the chi-square homogeneity test is equivalent to a two-tailed test that we discussed in an earlier chapter. What test is that?
The test is two proportionsz-test
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For a -curve with degrees of freedom determine the -value that has area.
a. to its right
b. to its right.
In each of Exercises 12.18-12.23, we have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distribution of the variable differs from the given distribution.
Distribution: 0.2, 0.4, 0.3, 0.1
Observed frequencies: 85, 215, 130, 70
Significance level = 0.05
AIDS Cases. According to the Centers for Disease Control and Prevention publication HIV Surveillance Report, the number of AIDS cases in the United States in 2011, by region and race, is as shown in the following contingency table.
| Region | White | Black | Other | Total |
| Northeast | 1,100 | 2,493 | 5,177 | |
| Northwest | 1,137 | 504 | 3221 | |
| South | 2,761 | 7,848 | 12,867 | |
| West | 764 | 1766 | 4,230 | |
| Total | 6052 | 25,435 |
a. How many cells does this contingency table have?
b. Fill in the missing entries.
c. What was the total number of AIDS cases in the United States in 2011?
d. How many AIDS cases were whites?
e. How many AIDS cases were Southerners?
f. How many AIDS cases were black Westerners?
HPV Vaccine. In the article "Correlates for Completic 3-dose Regimen of HPV Vaccine in Female Members of a Man Care Organization" (Mayo Clinical Proceedings, Vol. 84, Pp. 870 ), C. Chao et al. examined factors that may influence wh young female patients complete a three-injection sequence of the dasil quadrivalent human papillomavirus vaccine (HPV4). HPV virus that has been linked to the development of cervical cancer. following contingency table summarizes the data obtained for ' pletion of treatment versus practice type.
P.Noakes et al. researched the effects of fatty acids found in oily fish on lowering the risk of allergic disease in the article "Increased Intake of Oily Fish in Pregnancy: Effects on Neonatal Immune Responses and on Clinical Outcomes in Infants at Mo.". Pregnant women were randomly assigned to continue their habitual diet (control group), which was low in oily fish, or to consume two portions of salmon per week (treatment group). Their infants were clinically evaluated at months of age and the frequency of many different symptoms was recorded. Of the infants in the control group,had symptoms of dry skin; and of the 45 infants in the experimental group, had symptoms of dry skin. At thedata-custom-editor="chemistry" significance level, do the data provide sufficient evidence to conclude that a difference exists in the proportions of infants who have symptoms of dry skin at months between those whose mothers continue their habitual diet and those whose mothers consume two portions of salmon per week?
Part (a): Use the two-portionsz-test to perform the required hypothesis test.
Part (b): Use the chi-square homogeneity test to perform the required hypothesis test.
Part (c): Compare your results in parts (a) and (b).
Part (d): Explain what principle is being illustrated.
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