4.8 Those who gave parental consent easily may have been more affluent, better educated families who trusted vaccines and also had better hygiene or less exposure to tuberculosis.

4.18 The high-school seniors who take the SAT are not a random sample because this test is taken by students who intend to go to college; these are generally students with above-average scholastic aptitude. The relationship between the fraction of a state's seniors who take the SAT and the state's average SAT score is negative. If a small fraction of the state's seniors take the SAT, these will mostly be the state's best students. As the fraction of a state's students taking the SAT increases, the group of students who take the SAT is increasingly composed of weaker students, who bring down the state's average SAT.

4.34 Common sense says that these were not random samples. Those who ordered pitchers were surely planning on drinking a lot and fulfilled their objectives. Pitchers do exert some psychological pressure to finish what has been paid for, but surely big drinkers would still drink a lot even if they were forced to do so by the glass or bottle.

4.38 There is the potential for survivor bias here, in that some of the people hired in 1970 may no longer be with the firm and those who stayed may not be a random sample. For example, black employees may have been disproportionately fired, or they may have been disproportionately successful and hired away by other companies.

4.50 The people surveyed are not a randomly selected group who are asked to stay at Red Lion and then tell whether they would come back. Instead, the people surveyed are those who voluntarily chose Red Lion; this survey does not include anyone who tried Red Lion and never came back. Suppose that 1,000 people try Red Lion and that 49 decide to return and 951 do not. A survey is now made of 50 people--the 49 returnees plus one person trying Red lion for the first time. In this hypothetical example, 95.1% of the people who try Red Lion for the first time never go again, but 49 of 50 people now staying at Red Lion are returnees.