Many adults owe money from their college loans for years into their professional careers. A newspaper would like to estimate the proportion of all adults in the city who have debts from college loans. To collect data, a random sample of 300 young adults between the ages of 25 and 35 is asked, "Do you have more than $5,000 in current college debts?” 68% of those sampled reported that they do have more than $5,000 in college-related debts. How might this sample be biased in obtaining an estimate of all adults in the city who have college debts?
Answer
A
Because young adults were randomly selected, this sample should provide an unbiased estimate of the proportion of adults with college debts.
B
Because only young adults were sampled, undercoverage bias may cause the newspaper to overestimate the proportion of all adults who have college debts.
C
Because some young adults may not honestly report their debts, response bias may cause the newspaper to underestimate the proportion of adults with college debts.
D
Because adults with college debts may be less likely to respond, voluntary response bias may cause the newspaper to underestimate the proportion of adults who have college debts.
Explanation
The newspaper wants to estimate the proportion for all adults, but it sampled only people ages 25 to 35. Older adults are left out, so the sample may not represent the full adult population; this is undercoverage bias. Since younger adults may be more likely to have current college debt than older adults, the estimate could be too high. Thus, the choice describing undercoverage and possible overestimation is correct.
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