In: Statistics and Probability
The average student loan debt of a U.S. college student
at the end of four years of college is estimated to be about
$22,000. You take a random sample of 150 college students in the
state of Wyoming and find that the mean debt is $19,850, and the
sample standard deviation is $2,180.
(a) Construct a 95% confidence interval for the mean debt of all
Wyoming college graduates.
(b) Construct a 98% confidence interval for the mean debt of all
Wyoming college graduates.
(c) Is there evidence that the mean debt of all Wyoming college
graduates is significantly different from the national average? To
answer this research question, do the following:
(1) State the
hypotheses.
(2) Calculate the
test statistic.
(3) Estimate the
p-value, and state a decision.
(4) Using the
p-value, assess the strength of your decision.
(5) Answer the
research question.