Question

1. Based on past experience, a bank believes that 7% of the people who receive loans will not make payments on time. The bank takes a random sample of 200 recently approved loans.
   1. Find the quartiles of the sample proportions of clients who will not make timely payments.
   2. What values of sample proportions of clients who will not make timely payments would be unusual? Explain.
   3. Construct and interpret a 95% confidence interval for the true proportion of clients who will not make timely payments.
   4. Since the U.S. economy has changed, bank officials would like to do a new study to estimate the true proportion of clients who will not make timely payments. Assume you have no preconceived idea of what that proportion would be. What sample size is needed if you wish to be 99% confident that your estimate is within 2% of the true proportion.   
   5. Based on previous research, you assume the proportion of clients who will not make timely payments is 7%. What sample size is needed if you wish to be 99% confident that your estimate is within 2% of the true proportion.

Answer 1

proportion of the people who receive loans will not make payments on time. p=0.07

total number of sample taken n= 200

a)

Quartile 1

Quartile 2 is the 50th percentile

Quartile 3 is the 75th percentile

b) Sample proportion that is 3 standard deviation or more away from the mean is considered unusual.

sample proportion that is 0.016 or less and 0.124 or more can be considered unusual.

c)

for 95% confidence

d) Margin of error = 0.02

for 99% confidence

since the proportion is not mentioned p = 0.5

e) now p = 0.07