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

Use of Alternative Therapies by Education Level Education Level Percent Using Alternative Therapies High school or less 4.3%

College—1 to 4 years 8.2%

College—5 years or more 11.0%

These percentages were based on data from 7320 people whose education level was high school or less, 4793 people with 1 to 4 years of college, and 1095 people with 5 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.

Uses Alternative Therapies Does Not Use Alternative Therapies Total HS/less 7320 College: 1–4 yrs 4793 College: $5 yrs 1095

b. Construct a table of estimated probabilities by dividing the count in each of the six table cells by the total sample size, n 5 13,208.

c. The authors of the study indicated that the sample was selected in a way that makes it reasonable to regard the estimated probabilities in the table from Part

(b) as representative of the adult population in the United States. Use the information in that table to estimate the following probabilities for adults in the United States.
i. The probability that a randomly selected individual has 5 or more years of college.
ii. The probability that a randomly selected individual uses alternative therapies.
iii. The probability that a randomly selected individual uses alternative therapies given that he or she has 5 or more years of college.
iv. The probability that a randomly selected individual uses alternative therapies given that he or she has an education level of high school or less.
v. The probability that a randomly selected individual who uses alternative therapies has an education level of high school or less.
vi. The probability that a randomly selected individual with some college uses alternative therapies.

d. Are the events H 5 event that a randomly selected individual has an education level of high school or less and A 5 event that a randomly selected individual uses alternative therapies independent events? Explain.