Chapter 6.6, Problem 84E

The article “U.S. Investors Split Between Digital and Traditional Banking” (gallup.com, August 5, 2016, retrieved April 25, 2017) summarized data from a Gallup survey of a random sample of 1019 U.S. adults with investments of $10,000 or more. Based on the survey data, it was estimated that 31 % of investors manage their investments by doing everything they possibly can online. But the authors of the article also noted that there was quite a difference between younger investors (age 18 to 49) and older investors (age 50 and older). For younger investors, 43% said they do everything they possibly can online, while the percentage for older investors was 23%.

1. a. Use the given information to estimate P(O), P(O|Y), and P(O|F) where O = event that a randomly selected investor does everything possible online, Y = event that a randomly selected investor is age 18 to 49, and F = event that a ran do ml y selected investor is 50 years old or older.
2. b. Suppose that 40% of investors are between the ages of 18 and 49. Use the probabilities from Part (a) and the estimate P(Y) = 0.40 to calculate P(Y|O) and write a sentence interpreting this value.

6.81 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).

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

1. a. Use the information given to determine the number of respondents falling into each of the six cells of the table below.

1. b. Construct a table of estimated probabilities by dividing the count in each of the six table cells by the total sample size, n = 13,208.
2. 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.
   1. i. The probability that a randomly selected individual has 5 or more years of college.
   2. ii. The probability that a randomly selected individual uses alternative therapies.