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.
a. Only 354 of the 1000 respondents chose the correct answer of never. For
purposes of this exercise, you can 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 \(.40(40 \%) ?\)
Use \(\alpha=.05\) to test the appropriate hypotheses.
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 \(\alpha=.05\).