The accompanying table summarizes data from a medical expenditures survey carried out by the National Center for Health Statistics (€œAssessing the Effects of Race and Ethnicity on Use of Complementary and Alternative Therapies in the USA,€ Ethnicity and Health [2005]: 19€“ 32).

These percentages were based on data from 7,320 people whose education level was high school or less, 4,793 people with 1 to 4 years of college, and 1,095 people with = or more years of college.
a. Use the information given to determine the number of respondents falling into each of the six cells of the table below.

b. The authors of the study indicated that the sample was representative of the adult population in the United States. Estimate the following probabilities for adults in the United States.
i. The probability that a randomly selected adult has five or more years of college.
ii. The probability that a randomly selected adult uses alternative therapies.
iii. The probability that a randomly selected adult uses alternative therapies given that he or she has five or more years of college. iv. The probability that a randomly selected adult uses alternative therapies given that he or she has an education level of high school or less. v. The probability that a randomly selected adult who uses alternative therapies has an education level of high school or less.
vi. The probability that a randomly selected adult with some college uses alternative therapies.
c. Consider the events H = event that a randomly selected adult has an education level of high school or less and A = event that a randomly selected adult uses alternative therapies. Are these independent events? Explain.

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Use of Alternative Theraples by Education Level Education Level High school or less College-1 to 4 years College -5 years or more Percent using Alternative Theraples 4.3% 8.2 1 1.0% UsesDoes Not Use Alternative Alternative HS/Less College: 1-4Yrs College:2 5 Yrs Theraples Theraples Total 7,320 4.793 1,095