MS1023 Business Statistics with Computer Applications Homework #4

Maho Sonmez maho.sonmez@utsa.edu 1

MS1023 Business Statistics w/Comp Apps I

Homework #4 – Use Red Par Score Form

Chps. 9 & 10: 50 Questions Only

1. The first step in testing a hypothesis is to

establish a true null hypothesis and a false

alternative hypothesis.

a) True

b) False

2. In testing hypotheses, the researcher

initially assumes that the alternative

hypothesis is true and uses the sample data

to reject it.

a) True

b) False

3. The null and the alternative hypotheses

must be mutually exclusive and collectively

exhaustive.

a) True

b) False

4. Generally speaking, the hypotheses that

business researchers want to prove are stated

in the alternative hypothesis.

a) True

b) False

5. When a true null hypothesis is rejected,

the researcher has made a Type I error.

a) True

b) False

6. When a false null hypothesis is rejected,

the researcher has made a Type II error.

a) True

b) False

7. The rejection region for a hypothesis test

becomes smaller if the level of significance

is changed from 0.01 to 0.05.

a) True

b) False

8. Whenever hypotheses are established

such that the alternative hypothesis is “μ>8”,

where μ is the population mean, the

hypothesis test would be a two-tailed test.

a) True

b) False

9. Whenever hypotheses are established

such that the alternative hypothesis is “μ >

8″, where μ is the population mean, the p-

value is the probability of observing a

sample mean greater than the observed

sample mean assuming that μ ≥ 8.

a) True

b) False

10. If a null hypothesis was not rejected at

the 0.10 level of significance, it will be

rejected at a 0.05 level of significance based

on the same sample results.

a) True

b) False

11. Consider the following null and

alternative hypotheses.

Ho: 67

Ha: > 67

These hypotheses _______________.

a) indicate a one-tailed test with a rejection

area in the right tail

b) indicate a one-tailed test with a rejection

area in the left tail

c) indicate a two-tailed test

d) are established incorrectly

e) are not mutually exclusive

MS1023 Business Statistics with Computer Applications Homework #4

Maho Sonmez maho.sonmez@utsa.edu 2

12. Consider the following null and

alternative hypotheses.

Ho: p .16

Ha: p < .16

These hypotheses _______________.

a) indicate a one-tailed test with a rejection

area in the right tail

b) indicate a one-tailed test with a rejection

area in the left tail

c) indicate a two-tailed test

d) are established incorrectly

e) are not mutually exclusive

13. Suppose the alternative hypothesis in a

hypothesis test is: “the population mean is

less than 60″. If the sample size is 27, is

unknown, and alpha =.05, the critical value

of t is _______.

a) 2.0555

b) -2.0555

c) -1.7056

d) -1.7033

e) -2.0518

14. Suppose the alternative hypothesis in a

hypothesis test is “the population mean is

greater than 60″. If the sample size is 24,

is unknown, and alpha = .01, the critical

value of t is _______.

a) -2.8073

b) -2.7969

c) 2.8073

d) 2.4999

e) 2.4922

15. A researcher is testing a hypothesis of a

single mean. The critical t value for = .05 and a one-tailed test is 2.0639. The observed

t value from sample data is 1.742. The

decision made by the researcher based on

this information is to ______ the null

hypothesis.

a) reject

b) not reject

c) redefine

d) change the alternate hypothesis into

e) restate

16. A researcher is testing a hypothesis of a

single mean. The critical t value for = .05 and a two-tailed test is +2.0796. The

observed t value from sample data is -2.92.

The decision made by the researcher based

on this information is to _____ the null

hypothesis.

a) reject

b) not reject

c) redefine

d) change the alternate hypothesis into

e) restate

17. The diameter of 3.5 inch diskettes is

normally distributed. Periodically, quality

control inspectors at Dallas Diskettes

randomly select a sample of 16 diskettes. If

the mean diameter of the diskettes is too

large or too small the diskette punch is shut

down for adjustment; otherwise, the

punching process continues. The null

hypothesis is ______.

a) n 16

b) n = 16

c) = 3.5

d) 3.5

e) ≥ 3.5

18. The diameter of 3.5 inch diskettes is

normally distributed. Periodically, quality

control inspectors at Dallas Diskettes

randomly select a sample of 16 diskettes. If

the mean diameter of the diskettes is too

large or too small the diskette punch is shut

down for adjustment; otherwise, the

punching process continues. The last

sample showed a mean and standard

deviation of 3.55 and 0.08 inches,

MS1023 Business Statistics with Computer Applications Homework #4

Maho Sonmez maho.sonmez@utsa.edu 3

respectively. Using = 0.05, the appropriate decision is _______.

a) reject the null hypothesis and shut down

the punch

b) reject the null hypothesis and do not shut

down the punch

c) do not reject the null hypothesis and shut

down the punch

d) do not reject the null hypothesis and do

not shut down the punch

e) do nothing

The following data (in pounds), which were

selected randomly from a normally

distributed population of values, represent

measurements of a machine part that is

supposed to weigh, on average, 8.3 pounds.

8.1 8.4 8.3 8.2 8.5 8.6

8.4 8.3 8.4 8.2 8.8 8.2

8.2 8.3 8.1 8.3 8.4 8.5

8.5 8.7

Use these data and alpha = 0.01 to test the

hypothesis that the parts average 8.3 pounds.

Answer the questions 19-21 based on the

above information.

19. The null hypothesis is ______.

a) n 20

b) n = 20

c) = 8.3

d) 8.3

e) ≥ 8.3

20. The critical value is ______.

a) -2.8609

b) 2.8609

c) ±2.8453

d) ±2.5395

e) ±2.8609

21. Using = 0.01, the appropriate decision

is to _______ the null hypothesis.

a) reject

b) not reject

c) redefine

d) change the alternate hypothesis into

e) restate

Downtime in manufacturing is costly and

can result in late deliveries, backlogs, failure

to meet orders, and even loss of market

share. Suppose a manufacturing plant has

been averaging 23 minutes of downtime per

day for the past several years, but during the

past year, there has been a significant effort

by both management and production

workers to reduce downtime. In an effort to

determine if downtime has been

significantly reduced, company productivity

researchers have randomly sampled 31 days

over the past several months from company

records and have recorded the daily

downtimes shown below in minutes. Use

these data and an alpha of .01 to test to

determine if downtime has been

significantly reduced. Assume that daily

downtimes are normally distributed in the

population.

19 22 17 19 32 24

16 18 27 17 24 19

23 27 28 19 17 18

26 22 19 15 18 25

23 19 26 21 16 21

24

Answer the questions 22-25 based on the

above information.

22. The alternative hypothesis is ______.

a) = 23

MS1023 Business Statistics with Computer Applications Homework #4

Maho Sonmez maho.sonmez@utsa.edu 4

b) > 23

c) ≤ 23

d) 23

e) < 23

23. The critical value is ______.

a) -2.4528

b) 2.4528

c) 2.4573

d) -2.4573

e) ±2.7500

24. Using = 0.01, the appropriate decision

is to _______ the null hypothesis

a) reject

b) not reject

c) redefine

d) change the alternate hypothesis into

e) restate

25. Using = 0.05, the appropriate decision

is to _______ the null hypothesis

a) reject

b) not reject

c) redefine

d) change the alternate hypothesis into

e) restate

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 < 0.50

e) n > 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

b) 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

b) 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

41. A researcher wants to conduct a

before/after study on 11 subjects to

determine if a treatment results in any

difference in scores. The null hypothesis is

that the average difference is zero while the

alternative hypothesis is that the average

difference is not zero. Scores are obtained

on the subjects both before and after the

treatment. After subtracting the after scores

from the before scores, the average

difference is computed to be -2.40 with a

sample standard deviation of 1.21. Assume

that the differences are normally distributed

in the population. The degrees of freedom

for this test are _______.

a) 11

b) 2

c) 9

d) 20 e) 10

42. A researcher wants to conduct a

before/after study on 11 subjects to

determine if a treatment results in any

difference in scores. The null hypothesis is

that the average difference is zero while the

alternative hypothesis is that the average

difference is not zero. Scores are obtained

on the subjects both before and after the

treatment. After subtracting the after scores

from the before scores, the average

difference is computed to be -2.40 with a

sample standard deviation of 1.21. Assume

that the differences are normally distributed

in the population. The observed t value for

this test is _______.

a) -6.58

b) -21.82

c) -2.4

d) 1.98

e) 2.33

43. A researcher wants to conduct a

before/after study on 11 subjects to

determine if a treatment results in any

difference in scores. The null hypothesis is

that the average difference is zero while the

alternative hypothesis is that the average

difference is not zero. Scores are obtained

on the subjects both before and after the

treatment. After subtracting the after scores

from the before scores, the average

difference is computed to be -2.40 with a

sample standard deviation of 1.21. A 0.05

level of significance is selected. Assume

that the differences are normally distributed

in the population. The table t value for this

test is _______.

a) ±1.8125

b) ±2.2622

c) ±1.7959

d) ±2.2281

e) ±3.1693

One of the new thrusts of quality control

management is to examine the process by

which a product is produced. This approach

also applies to paperwork. In industries

where large long-term projects are

undertaken, days and even weeks may

elapse as a change order makes its way

through a maze of approvals before

receiving final approval. This process can

result in long delays and stretch schedules to

the breaking point. Suppose a quality control

consulting group claims that it can

significantly reduce the number of days

required for such paperwork to receive

approval. In an attempt to “prove” its case,

the group selects five jobs for which it

revises the paperwork system. The following

data show the number of days required for a

change order to be approved before the

group intervened and the number of days

required for a change order to be approved

MS1023 Business Statistics with Computer Applications Homework #4

Maho Sonmez maho.sonmez@utsa.edu 8

after the group instituted a new paperwork

system.

Before After

12 8

7 3

10 8

16 9

8 5

Use alpha = 0.05 to determine whether there

was a significant drop in the number of days

required to process paperwork to approve

change orders. Assume that the differences

in days are normally distributed.

Answer the questions 44-50 based on the

above information.

44. The null hypothesis for this problem is

_____.

a) D = 0

b) D ≥ 0

c) D ≤ 0

d) D ≠ 0

e) D ≥ 1

45. The degrees of freedom in this problem

are _______.

a) 3

b) 8

c) 5

d) 9

e) 4

46. The sample standard deviation (sd) of the

differences is _______.

a) 1.6733

b) 1.6373

c) 1.8807

d) 1.8708

e) 1.8078

47. What is the appropriate critical value for

this problem for alpha = 0.01?

a) 4.6041

b) 4.0321

c) 3.3649

d) 4.5407

e) 3.7469

48. Mean sample difference (�̅�) is _______.

a) 10.6

b) 6.6

c) 4

d) -4

e) 17.2

49. The observed value of t for this problem

is __________.

a) 4.78

b) 2.05

c) 4.87

d) -4.78

e) -2.05

50. The appropriate conclusion for this

problem is ___________.

a) not reject the null hypothesis, D ≤ 0

b) reject the null hypothesis, D ≥ 0

c) reject the null hypothesis D = 0

d) reject the null hypothesis, D ≤ 0

e) not reject the null hypothesis D ≥ 0