# MS1023 Business Statistics with Computer Applications Homework #4

August 30, 2017

uestion
26. Ophelia O’Brien, VP of Consumer
Credit of American First Banks (AFB),
monitors the default rate on personal loans
at the AFB member banks. One of her
standards is “no more than 5% of personal
loans should be in default.” On each Friday,
the default rate is calculated for a sample of
500 personal loans. Last Friday’s sample
contained 30 defaulted loans. The null
hypothesis is _______.
a) p ? 0.05
b) p ? 0.05
c) p > 0.05
d) p < 0.05
e) p = 0.05
27. Ophelia O'Brien, VP of Consumer
Credit of American First Banks (AFB),
monitors the default rate on personal loans
at the AFB member banks. One of her
standards is "no more than 5% of personal
loans should be in default." On each Friday,
the default rate is calculated for a sample of
500 personal loans. Last Friday's sample
contained 30 defaulted loans. Using ? =
0.10, the critical z value is _______.
a) 1.645
b) -1.645
c) 1.28
d) -1.28
e) 2.28
28. Ophelia O'Brien, VP of Consumer
Credit of American First Banks (AFB),
monitors the default rate on personal loans
at the AFB member banks. One of her
standards is "no more than 5% of personal
loans should be in default." On each Friday,
the default rate is calculated for a sample of
500 personal loans. Last Friday's sample
contained 30 defaulted loans. Using ? =
0.10, the observed z value is _______.
a) 1.03
b) -1.03
c) 0.046
d) -0.046
e) 1.33
29. Ophelia O'Brien, VP of Consumer
Credit of American First Banks (AFB),
monitors the default rate on personal loans
at the AFB member banks. One of her
standards is "no more than 5% of personal
loans should be in default." On each Friday,
the default rate is calculated for a sample of
500 personal loans. Last Friday's sample
MS1023 Business Statistics with Computer Applications Homework #4
Maho Sonmez maho.sonmez@utsa.edu 5
contained 30 defaulted loans. Using ? =
0.10, the appropriate decision is _______.
a) reduce the sample size
b) increase the sample size
c) reject the null hypothesis
d) do not reject the null hypothesis
e) do nothing
30. Ophelia O'Brien, VP of Consumer
Credit of American First Banks (AFB),
monitors the default rate on personal loans
at the AFB member banks. One of her
standards is "no more than 5% of personal
loans should be in default." On each Friday,
the default rate is calculated for a sample of
500 personal loans. Last Friday's sample
contained 38 defaulted loans. Using ? =
0.10, the appropriate decision is _______.
a) reduce the sample size
b) increase the sample size
c) reject the null hypothesis
d) do not reject the null hypothesis
e) do nothing
31. The executives of CareFree Insurance,
Inc. feel that "a majority of our employees
perceive a participatory management style at
CareFree." A random sample of 200
CareFree employees is selected to test this
hypothesis at the 0.05 level of significance.
Eighty employees rate the management as
participatory. The null hypothesis is
__________.
a) p ? 40
b) p < 40
c) p ? 0.50
d) p 200
32. A study by Hewitt Associates showed
that 79% of companies offer employees
flexible scheduling. Suppose a researcher
believes that in accounting firms this figure
is lower. The researcher randomly selects
415 accounting firms and through interviews
determines that 303 of these firms have
flexible scheduling. With a 1% level of
significance, does the test show enough
evidence to conclude that a significantly
lower proportion of accounting firms offer
employees flexible scheduling?
a) Reject the null hypothesis, concluding
that the lower proportion of accounting
firms offer employees flexible scheduling.
b) Do not reject the null hypothesis,
concluding that the lower proportion of
accounting firms offer employees flexible
scheduling.
c) Reject the null hypothesis, concluding
that the higher proportion of accounting
firms offer employees flexible scheduling.
d) Do not reject the null hypothesis,
concluding that the higher proportion of
accounting firms offer employees flexible
scheduling.
e) The test is inconclusive.
Suppose a Realtor is interested in comparing
the asking prices of midrange homes in
Peoria, Illinois, and Evansville, Indiana. The
Realtor conducts a small telephone survey in
the two cities, asking the prices of midrange
homes. A random sample of 21 listings in
Peoria resulted in a sample average price of
\$116,900, with a standard deviation of
\$2,300. A random sample of 26 listings in
Evansville resulted in a sample average
price of \$114,000, with a standard deviation
of \$1,750. The Realtor assumes prices of
midrange homes are normally distributed
and the variance in prices in the two cities is
about the same. The researcher wishes to
test whether there is any difference in the
mean prices of midrange homes of the two
cities for alpha = .01.
MS1023 Business Statistics with Computer Applications Homework #4
Maho Sonmez maho.sonmez@utsa.edu 6
Answer the questions 33-36 based on the
above information.
33. The null hypothesis for this problem is
______.
a) ?1 – ?2 0
c) ?1 – ?2 = 1
d) ?1 – ?2 ? 0
e) ?1 – ?2 = 0
34. The degrees of freedom for this problem
are _______.
a) 20
b) 25
c) 46
d) 45
e) 43
35. The critical t value from table is ____.
a) ±2.6870
b) ±2.6896
c) ±2.4121
d) ±2.0141
e) ±1.6794
36. The appropriate decision for this
problem is to _____________.
a) not reject the null hypothesis, ?1 – ?2 = 0
b) reject the null hypothesis, ?1 – ?2 ? 0
c) reject the null hypothesis ?1 – ?2 = 0
d) not reject the null hypothesis, ?1 – ?2 ? 0
e) reject the null hypothesis ?1 – ?2 = 1
Based on an indication that mean daily car
rental rates may be higher for Boston than
for Dallas, a survey of eight car rental
companies in Boston is taken and the sample
mean car rental rate is \$47, with a standard
deviation of \$3. Further, suppose a survey of
nine car rental companies in Dallas results in
a sample mean of \$44 and a standard
deviation of \$3. Use alpha = 0.05 to test to
determine whether the average daily car
rental rates in Boston are significantly higher
than those in Dallas. Assume car rental rates
are normally distributed and the population
variances are equal.
Answer the questions 37-40 based on the
above information.
37. The null hypothesis for this problem is
______.
a) ?1 – ?2 0
c) ?1 – ?2 = 1
d) ?1 – ?2 ? 0
e) ?1 – ?2 = 0
38. The degrees of freedom for this problem
are _______.
a) 7
b) 8
c) 9
d) 15
e) 16
39. The critical t value from table is ____.
a) -1.7531
b) 1.7531
c) -2.1314
d) 2.1314
e) ±1.6794
40. The appropriate decision for this
problem is to _____________.
a) not reject the null hypothesis, ?1 – ?2 ? 0
b) reject the null hypothesis, ?1 – ?2 ? 0
c) reject the null hypothesis ?1 – ?2 = 0
MS1023 Business Statistics with Computer Applications Homework #4
Maho Sonmez maho.sonmez@utsa.edu 7
d) reject the null hypothesis, ?1 – ?2 ? 0
e) not reject the null hypothesis ?1 – ?2 ? 0

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