SOLUTION: We are interested in finding out what proportion of borrowers default on a credit card loan. We sample 100 credit cards. We find that 10 default. (A) Find proportion of credit car

Question 1204924: We are interested in finding out what proportion of borrowers default on a credit card loan. We sample 100 credit cards. We find that 10 default.
(A) Find proportion of credit card borrowers that default
(B) Construct a 80% Confidence Interval
(C) Construct a 99% Confidence Interval
(D) What does your findings interpret?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
sample size is 100.
10 out of the 100 default.
that's a mean proportion of .1
standard error is equal to sqrt(.1 * .9 / 100) = .03
critical z-score for 80% confidence interval is z = plus or minus 1.28155.
critical z-score for 90% confidence interval is z = plus or minus 1.64485.
z-score formula is z = (x-m)/s
z is the z-score.
x is the critical proportion.
m is the mean proportion.
s is the standard error.
you have z.
you need to solve for x.

at 80% confidence interval:
the high side of the confidence interval formula is 1.28155 = (x - .1) / .03.
solve for x to get x = 1.28155 * .03 + .1 = .1384465.
the low side of the confidence interval formula is -1.28155 = (x - .1) / .03.
solve for x to get x = -1.28155 * .03 + .1 = .0615535.
your 80% confidence interval is from .0615535 to .1384465.

at 90% confidence interval:
the high side of the confidence interval formula is 1.64485 = (x - .1) / .03.
solve for x to get x = 1.64485 * .03 + .1 = .1493455.
the low side of the confidence interval formula is -1.64485 = (x - .1) / .03.
solve for x to get x = -1.64485 * .03 + .1 = .0506545.
your 90% confidence interval is from .0506545 to .1493455.

here's what 80% and 90% confidence intervals look like on a graph.
the mean proportion is .1 (10/100 = .1)
the standard error is .03 (sqrt(.1*.9/100))

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