# MS1023 Business Statistics with Computer Applications Homework #4

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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