A paper included analysis of data from a national sample of 1,000 Americans. One question on the survey is given below. "You owe $3,000 on your credit card. You pay a minimum payment of $30 each...

A paper included analysis of data from a national sample of 1,000 Americans. One question on the survey is given below.

"You owe $3,000 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.

Only 355 of the 1,000 respondents chose the correct answer of "never." 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 the five-step process for hypothesis testing (HMC³) described in this section and

to test the appropriate hypotheses.

The paper also reported that 37.2% of those in the sample chose one of the wrong answers (a, b, or 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

(Round your test statistic to two decimal places and yourP-value to four decimal places.)