A paper included analysis of data from a national sample of 1000 Americans. One
ID: 3362336 • Letter: A
Question
A paper included analysis of data from a national sample of 1000 Americans. One question on the survey is given below.
"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 357 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 0.40 (40%)? Use
= 0.05
to test the appropriate hypotheses. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z=
P-Value=
(b) The paper also reported that 37.9% 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
= 0.05.
(Round your test statistic to two decimal places and your P-value to four decimal places.)
z=
P-value=
Explanation / Answer
(A) Below are the null and alternate hypothesis
H0: p >= 0.4
h1: p < 0.4
test statistics, z = (0.357 - 0.4)/sqrt(0.4*0.6/1000) = -2.7756
p-value = 0.00275
As p-value is less than significance level 0.05, we reject the null hypothesis.
this means there are sufficient evidence to conclude that less than 40% of adult Americans who can answer the question correctly.
(B) Below are the null and alternate hypothesis
H0: p <= 0.33
h1: p > 0.33
test statistics, z = (0.379 - 0.333)/sqrt(0.333*0.667/1000) = 3.086
p-value = 0.001
As p-value is less than significance level 0.05, we reject the null hypothesis.
this means there is significant evidence to conclude that more than one-third adult Americans would select a wrong answer to this question.
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