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Chapter 12: Q. 12.11 (page 491)
In each case, decide whether Assumptions and for using chi-square goodness-of-fit test are satisfied.
Sample size: .
Relative frequencies:.
Both Assumptionandare satisfied.
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Suppose that you have bivariate data for an entire population.
a. How would you decide whether an association exists between the two variables under consideration?
b. Assuming that you make no calculation mistakes, could your conclusion be in error? Explain your answer.
12.53 AIDS Cases. Refer to Exercise 12.47. For AIDS cases in the United States in 2011, solve the following problems:
| 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. Find and interpret the conditional distributions of region by race.
b. Find and interpret the marginal distribution of region.
c. Are the variables "region" and "race" associated? Explain your answer.
d. What percentage of AIDS cases were in the South?
e. What percentage of AIDS cases among whites were in the South?
f. Without doing further calculations, respond true or false to the distributions of race by region are not identical.
g. Find and interpret the marginal distribution of race and the conditional distributions of race by region.
Why is the phrase "goodness of fit" used to describe the type of hypothesis test considered in this section?
How do you identify different chi-square distributions?
Variegated Plants. Arabidopsis is a genus of flowering plants related to cabbage. A variegated mutant of the Arabidopsis has yellow streaks or marks. E. Miura et al. studied the origin of this variegated mutant in the article "The Balance between Protein Synthesis and Degradation in Chloroplasts Determines Leaf Variegation in Arabidopsis yellow variegated Mutants" (The Plant Cell, Vol. 19, No. 4, pp. 1313-1328). In a second-generation cross of variegated plants, 216 were variegated and 84 were normal. Genetics predicts that 75% of crossed variegated plants would be variegated and 25% would be normal. At the 10% significance level, do the data provide sufficient evidence to conclude that the second generation of crossed variegated plants does not follow the genetic predictions?
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