Chapter 10.3, Problem 30E

The paper “Debt Literacy, Financial Experiences and Over-Indebtedness” (Social Science Research Network, Working paper W14808, 2008) included analysis of data from a national sample of 1000 Americans. One question on the survey was:

“You owe $3000 on your credit card. You pay a minimum payment of $30 each month. At an Annual Percentage Rate of 12% (or 1% per month), how many years would it take to eliminate your credit card debt if you made no additional charges?”

Answer options for this question were: (a) less than 5 years; (b) between 5 and 10 years; (c) between 10 and 15 years; (d) never—you will continue to be in debt; (e) don’t know; and (f) prefer not to answer.

1. a. Only 354 of the 1000 respondents chose the correct answer of never. For purposes of this exercise, assume that the sample is representative of adult Americans. Is there convincing evidence that the proportion of adult Americans who can answer this question correctly is less than 0.40 (40%)? Use α = 0.05 to test the appropriate hypotheses. (Hint: See Example 10.10.)
2. b. The paper also reported that 37.8% of those in the sample chose one of the wrong answers (a, b, and c) as their response to this question. Is it reasonable to conclude that more than one-third of adult Americans would select a wrong answer to this question? Use α = 0.05.