Refer to Exercise 2.25. The agreement between the percentages for the randomized study and the actual population percentages for various groups of people may allow us to have more confidence in the main results of the survey, which are the percentages of various HIV-related risk groups as shown next. a. For the nation as a whole, what percentage of those between the ages of 18 and 75 are at risk HIV infection? What is the percentage for the high -risk cities? (Actually, these percentages go much higher if sexual practices for more than the past year are taken into account.) b. The percentages can be used as estimates of probabilities for anticipating what might happen in certain situations. For example, if a national firm is to hire 1000 workers across the country, how many, would they expect to be at risk for HIV infection? What happens to this expected value if the firm hires all 1000 workers in high -risk cities? Solution BY RISK GROUP Gay, bisexual, and other men who have sex with men (MSM) of all races and ethnicities remain the population most profoundly affected by HIV. In 2010, the estimated number of new HIV infections among MSM was 29,800, a significant 12% increase from the 26,700 new infections among MSM in 20082. Although MSM represent about 4% of the male population in the United States4, in 2010, MSM accounted for 78% of new HIV infections among males and 63% of all new infections2. MSM accounted for 54% of all people living with HIV infection in 2011, the most recent year these data are available1. In 2010, white MSM continued to account for the largest number of new HIV infections (11,200), by transmission category, followed closely by black MSM (10,600)2. The estimated number of new HIV infections was greatest among MSM in the youngest age group. In 2010, the greatest number of new HIV infections (4,800) among MSM occurred in young black/African American MSM aged 13.