Question
In: Statistics and Probability
A large bank claims that approximately 14% of all house loans it issues are in default....
A large bank claims that approximately 14% of all house loans it issues are in default. A random sample of 243 house loans issued by this bank finds that 42 of them are in default. Do the data indicate that the proportion of loans in default exceeds 14%?
(a) State the null and alternative hypotheses for the test.
(b) State the formula for the test statistic and compute its value. Justify your answer.
(c) Construct the rejection region and make a decision. Use α = 0.05
(d) State a conclusion about the the proportion of house loans in default based on the test you performed.
Solutions
orchestra answered 2 years agoRelated Solutions
A large bank claims that approximately 14% of all house loans it issues are in default....
A large bank claims that approximately 14% of all house loans it
issues are in default. A random sample of 243 house loans issued by
this bank finds that 42 of them are in default. Do the data
indicate that the proportion of loans in default exceeds 14%?
(a) State the null and alternative hypotheses for the test.
(b) State the formula for the test statistic and compute its
value. Justify your answer.
(c) Construct the rejection region and make...
A bank makes loans to small businesses and on average 4.1% of them default on their...
A bank makes loans to small businesses and on average 4.1% of
them default on their loans within five years. The bank makes
provision for these losses when it makes its financial plans. The
Vice President in charge of small business loans thinks that the
default rate may be going down and gives you a random sample of 255
recent loans of which 7 defaulted within five years. What advice do
you give to the Vice President?
The probability that...
The recent default rate on all student loans is 6.2 percent. In a recent random sample...
The recent default rate on all student loans is 6.2 percent. In
a recent random sample of 314 loans at private universities, there
were 8 defaults.
Does this sample show sufficient evidence that the private
university loan default rate is below the rate for all
universities, using a left-tailed test at α = .010?
(a-1)
Choose the appropriate hypothesis.
a.
H0: ππ
≥ .062; H1: ππ < .062. Accept
H0 if z < –2.326
b.
H0: ππ
≥ .062; H1:...
The Sketchy Loner is a bank that issues 6 types of loans. In addition, to diversify...
The Sketchy Loner is a bank that issues 6 types of loans. In
addition, to diversify its portfolio and minimize its risk, the
bank invests in risk-free securities. The 6 loan types and the
risk-free securities with their annual rates of return are given
below:
Type of Loan or Security
Annual Rate of Return (%)
Home Mortgage (first)
12%
Home Mortgage (second)
13%
Commercial loan
16%
Auto Loan
16%
Home Improvement Loan
19%
Risk Free Security
11.5%
The bank’s objective...
The Sketchy Loner is a bank that issues 6 types of loans. In addition, to diversify...
The Sketchy Loner is a bank that issues 6 types of loans. In
addition, to diversify its portfolio and minimize its risk, the
bank invests in risk-free securities. The 6 loan types and the
risk-free securities with their annual rates of return are given
below:
Type of Loan or Security
Annual Rate of Return (%)
Home Mortgage (first)
12%
Home Mortgage (second)
13%
Commercial loan
16%
Auto Loan
16%
Home Improvement Loan
19%
Risk Free Security
11.5%
The bank’s objective...
The mortgage department of a large bank is interested in the nature of loans of first-time...
The mortgage department of a large bank is interested in the
nature of loans of first-time borrowers. This information will be
used to tailor their marketing strategy. They believe that the
probability that the first-time borrowers take out smaller loans
than other borrowers is 0.52. They perform a hypothesis test to
determine if the probability is the same or different from 0.52.
They sample 118 first-time borrowers and find 82 of these loans are
smaller that the other borrowers. What...
A bank president claims that the median of debt-to-equity ratio of commercial loans provided is less...
A bank president claims that the median of debt-to-equity ratio
of commercial loans provided is less than 5. A random sample of 15
commercial loans is selected with the following values for this
ratio:
1.31
1.33
1.22
1.78
1.45
1.32
1.46
1.41
1.19
1.05
1.29
1.11
1.37
1.21
1.65
Use a Sign Test at the 0.05 level to test this claim. DO THIS BY
HAND and not using Excel.
A bank president claims that the median of debt-to-equity ratio of commercial loans provided is less...
A bank president
claims that the median of debt-to-equity ratio of commercial loans
provided is less than 5. A random sample of 15 commercial loans is
selected with the following values for this ratio:
1.31
1.33
1.22
1.78
1.45
1.32
1.46
1.41
1.19
1.05
1.29
1.11
1.37
1.21
1.65
Use a Sign Test at
the 0.05 level to test this claim. Do this by hand and not using
Excel.
Straight bank loan. Left Bank has a standing rate of 7.7 (APR) for all bank loans...
Straight bank loan. Left Bank has a standing rate of 7.7 (APR)
for all bank loans and requires monthly payments. What is the
monthly payment if a loan is for (a) $130,000 for 6 years, (b)
$295,000 for 9 years, or (c) $1,300,000 for 23 years? What is
the effective annual rate of each of these loans?
Left Bank has a standing rate of 7.9% (APR) for all bank loans and requires monthly...
Left Bank has a standing rate of 7.9% (APR) for all bank loans
and requires monthly payments. What is the monthly payment if a
loan is for
(a) $140,000 for 5 years
(b) $255,000 for 10 years
(c) $1,500,000 for 25 years
What is the effective annual rate of each of these loans?
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