STAT125-HK. BUSINESS STATISTICS (STAT125-HK) > TAKE ASSESSMENT: MIDTERM EXAM

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1

The probability that house sales will increase in the next 6 months is estimated to be 0.25. The

probability that the interest rates on housing loans will go up in the same period is estimated to

be 0.74. The probability that house sales or interest rates will go up during the next 6 months is

estimated to be 0.89. The probability that house sales will increase but interest rates will not

during the next 6 months is:

a. 0.065

b. 0.15

c. 0.51

d. 0.89

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2

The process of using sample statistics to draw conclusions about true population parameters is

called

a. statistical inference.

b. the scientific method.

c. sampling.

d. descriptive statistics.

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3

Which of the following is NOT a reason for obtaining data?

a. Data are needed to formulate a statistical model.

b. Data are needed to evaluate conformance to standards.

c. Data are needed to measure performance of an ongoing production process.

d. Data are needed to provide input to a study.

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4

A catalog company that receives the majority of its orders by telephone conducted a study to

determine how long customers were willing to wait on hold before ordering a product. The

length of time was found to be a random variable best approximated by an exponential

distribution with a mean equal to 3 minutes. What proportion of customers having to hold more

than 1.5 minutes will hang up before placing an order?

a. 0.86466

b. 0.60653

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c. 0.39347

d. 0.13534

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5

Selection of raffle tickets from a large bowl is an example of

a. sampling with replacement.

b. sampling without replacement.

c. subjective probability.

d. None of the above.

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6

The width of each bar in a histogram corresponds to the

a. differences between the boundaries of the class.

b. number of observations in each class.

c. midpoint of each class.

d. percentage of observations in each class.

Question

7

If two events are mutually exclusive and collectively exhaustive, what is the probability that one

or the other occurs?

a. 0.

b. 0.50.

c. 1.00.

d. Cannot be determined from the information given.

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8

Which of the following is not an element of descriptive statistical problems?

a. An inference made about the population based on the sample.

b. The population or sample of interest.

c. Tables, graphs, or numerical summary tools.

d. Identification of patterns in the data.

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9

Which of the following statistics is not a measure of central tendency?

a. Mean.

b. Median.

c. Mode.

d. Q3.

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10

Major league baseball salaries averaged $1.5 million with a standard deviation of $0.8 million

in 1994. Suppose a sample of 100 major league players was taken. Find the approximate

probability that the average salary of the 100 players exceeded $1 million.

a. Approximately 0

b. 0.2357

c. 0.7357

d. Approximately 1

Question 11

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If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is

the probability that event A occurs?

a. 0.

b. 0.50.

c. 1.00.

d. Cannot be determined from the information given.

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2 points

12

TABLE 2-6

A sample of 200 students at a Big-Ten university was taken after the midterm to ask them

whether they went bar hopping the weekend before the midterm or spent the weekend

studying, and whether they did well or poorly on the midterm. The following table contains the

result.

Did Well on Midterm Did Poorly on Midterm

Studying for Exam 80

20

Went Bar Hopping 30

70

Referring to Table 2-6, of those who did well on the midterm in the sample, _______ percent of

them went bar hopping the weekend before the midterm.

a. 15

b. 27.27

c. 30

d. 50

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13

TABLE 2-5

The following are the durations in minutes of a sample of long-distance phone calls made

within the continental United States reported by one long-distance carrier.

Time (in Minutes)

Relative Frequency

0 but less than 5

0.37

5 but less than 10

0.22

10 but less than 15 0.15

15 but less than 20 0.10

20 but less than 25 0.07

25 but less than 30 0.07

30 or more

0.02

Referring to Table 2-5, what is the width of each class?

a. 1 minute

b. 5 minutes

c. 2%

d. 100%

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14

According to a survey of American households, the probability that the residents own 2 cars if

annual household income is over $25,000 is 80%. Of the households surveyed, 60% had

incomes over $25,000 and 70% had 2 cars. The probability that annual household income is

over $25,000 if the residents of a household do not own 2 cars is:

a. 0.12

b. 0.18

c. 0.40

d. 0.55

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15

A study is under way in Yosemite National Forest to determine the adult height of American

pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching

heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American

pines. The study involves collecting heights from 250 randomly selected adult American pine

trees and analyzing the results. Identify the population from which the study was sampled.

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a. The 250 randomly selected adult American pine trees.

b. The 25,000 adult American pine trees in the forest.

c. All the adult American pine trees taller than 60 feet.

d. All American pine trees, of any age, in the forest.

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16

When extreme values are present in a set of data, which of the following descriptive summary

measures are most appropriate?

a. CV and range.

b. mean and standard deviation.

c. interquartile range and median.

d. variance and interquartile range.

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17

A population frame for a survey contains a listing of 72,345 names. Using a table of random

numbers, how many digits will the code numbers for each member of your population contain?

a. 3

b. 4

c. 5

d. 6

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18

A recent survey of banks revealed the following distribution for the interest rate being charged

on a home loan (based on a 30-year mortgage with a 10% down payment).

Interest Rate: 7.0% 7.5% 8.0% 8.5% >8.5%

Probability

0.12 0.23 0.24 0.35 0.06

If a bank is selected at random from this distribution, what is the chance that the interest rate

charged on a home loan will exceed 8.0%?

a. 0.06

b. 0.41

c. 0.59

d. 1.00

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19

Referring to the histogram from Table 2-3, how many graduating seniors attended the

luncheon?

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a. 4

b. 152

c. 275

d. 388

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20

TABLE 2-4

A survey was conducted to determine how people rated the quality of programming available

on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to

100 (extremely good quality). The stem-and-leaf display of the data is shown below.

Stem Leaves

3

24

4

03478999

5

0112345

6

12566

7

01

8

9

2

Referring to Table 2-4, what percentage of the respondents rated overall television quality with

a rating between 50 and 75?

a. 0.11

b. 0.40

c. 0.44

d. 0.56

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21

The Central Limit Theorem is important in statistics because

a. for a large n, it says the population is approximately normal.

b. for any population, it says the sampling distribution of the sample mean is

approximately normal, regardless of the sample size.

c. for a large n, it says the sampling distribution of the sample mean is approximately

normal, regardless of the shape of the population.

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d. for any sized sample, it says the sampling distribution of the sample mean is

approximately normal.

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22

If you were constructing a 99% confidence interval of the population mean based on a sample

of n = 25 where the standard deviation of the sample s = 0.05, the critical value of t will be

a. 2.7969

b. 2.7874

c. 2.4922

d. 2.4851

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23

A statistics student found a reference in the campus library that contained the median family

incomes for all 50 states. She would report her data as being collected using

a. a designed experiment.

b. observational data.

c. a random sample.

d. a published source.

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24

TABLE 2-5

The following are the durations in minutes of a sample of long-distance phone calls made

within the continental United States reported by one long-distance carrier.

Time (in Minutes)

Relative Frequency

0 but less than 5

0.37

5 but less than 10

0.22

10 but less than 15 0.15

15 but less than 20 0.10

20 but less than 25 0.07

25 but less than 30 0.07

30 or more

0.02

Referring to Table 2-5, if 10 calls lasted 30 minutes or more, how many calls lasted less than 5

minutes?

a. 10

b. 185

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c. 295

d. 500

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25

The employees of a company were surveyed on questions regarding their educational

background and marital status. Of the 600 employees, 400 had college degrees, 100 were

single, and 60 were single college graduates. The probability that an employee of the

company is single or has a college degree is:

a. 0.10

b. 0.25

c. 0.667

d. 0.733

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26

The probability that house sales will increase in the next 6 months is estimated to be 0.25. The

probability that the interest rates on housing loans will go up in the same period is estimated to

be 0.74. The probability that house sales or interest rates will go up during the next 6 months

is estimated to be 0.89. The probability that neither house sales nor interest rates will increase

during the next 6 months is:

a. 0.11

b. 0.195

c. 0.89

d. 0.90

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27

A confidence interval was used to estimate the proportion of statistics students that are

females. A random sample of 72 statistics students generated the following 90% confidence

interval: (0.438, 0.642). Based on the interval above, is the population proportion of females

equal to 0.60?

a. No, and we are 90% sure of it.

b. No. The proportion is 54.17%.

c. Maybe. 0.60 is a believable value of the population proportion based on the

information above.

d. Yes, and we are 90% sure of it.

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28

Since a _______ is not a randomly selected probability sample, there is no way to know how

well it represents the overall population.

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a. simple random sample

b. quota sample

c. stratified sample

d. cluster sample

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29

TABLE 2-6

A sample of 200 students at a Big-Ten university was taken after the midterm to ask them

whether they went bar hopping the weekend before the midterm or spent the weekend

studying, and whether they did well or poorly on the midterm. The following table contains the

result.

Did Well on Midterm Did Poorly on Midterm

Studying for Exam 80

20

Went Bar Hopping 30

70

Referring to Table 2-6, _______ percent of the students in the sample went bar hopping the

weekend before the midterm and did well on the midterm.

a. 15

b. 27.27

c. 30

d. 50

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30

The collection of all possible events is called

a. a simple probability.

b. a sample space.

c. a joint probability.

d. the null set.

Question

31

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab

conducts. Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per

week. Interpret this value.

a. Most of the weeks resulted in rat costs of $13.00.

b. The median cost for the distribution of rat costs is $13.00.

c. The expected or average cost for all weekly rat purchases is $13.00.

d. The rat cost that occurs more often than any other is $13.00.

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32

Which of the following is not true about the Student’s t distribution?

a. It has more area in the tails and less in the center than does the normal distribution.

b. It is used to construct confidence intervals for the population mean when the

population standard deviation is known.

c. It is bell shaped and symmetrical.

d. As the number of degrees of freedom increases, the t distribution approaches the

normal distribution.

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33

If two events are mutually exclusive, what is the probability that one or the other occurs?

a. 0.

b. 0.50.

c. 1.00.

d. Cannot be determined from the information given.

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34

Tim was planning for a meeting with his boss to discuss a raise in his annual salary. In

preparation, he wanted to use the Consumer Price Index to determine the percentage

increase in his salary in terms of real income over the last three years. Which of the 4 methods

of data collection was involved when he used the Consumer Price Index?

a. Published sources

b. Experimentation

c. Surveying

d. Observation

Question

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35

A professor of economics at a small Texas university wanted to determine what year in school

students were taking his tough economics course. Shown below is a pie chart of the results.

What percentage of the class took the course prior to reaching their senior year?

a. 14%

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b. 44%

c. 54%

d. 86%

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36

TABLE 2-5

The following are the durations in minutes of a sample of long-distance phone calls made

within the continental United States reported by one long-distance carrier.

Time (in Minutes)

Relative Frequency

0 but less than 5

0.37

5 but less than 10

0.22

10 but less than 15 0.15

15 but less than 20 0.10

20 but less than 25 0.07

25 but less than 30 0.07

30 or more

0.02

Referring to Table 2-5, if 100 calls were randomly sampled, how many calls lasted 15 minutes

or longer?

a. 10

b. 14

c. 26

d. 74

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37

The chancellor of a major university was concerned about alcohol abuse on her campus and

wanted to find out the portion of students at her university who visited campus bars every

weekend. Her advisor took a random sample of 250 students. The portion of students in the

sample who visited campus bars every weekend is an example of __________.

a. a categorical random variable.

b. a discrete random variable.

c. a parameter.

d. a statistic.

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38

Which of the following statements about the median is not true?

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a. It is more affected by extreme values than the mean.

b. It is a measure of central tendency.

c. It is equal to Q2.

d. It is equal to the mode in bell-shaped "normal" distributions.

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39

Most analysts focus on the cost of tuition as the way to measure the cost of a college

education. But incidentals, such as textbook costs, are rarely considered. A researcher at

Drummand University wishes to estimate the textbook costs of first-year students at

Drummand. To do so, she monitored the textbook cost of 250 first-year students and found

that their average textbook cost was $300 per semester. Identify the sample in the study.

a. All Drummand University students.

b. All college students.

c. All first-year Drummand University students.

d. The 250 students that were monitored.

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40

The head librarian at the Library of Congress has asked her assistant for an interval estimate

of the mean number of books checked out each day. The assistant provides the following

interval estimate: from 740 to 920 books per day. If the head librarian knows that the

population standard deviation is 150 books checked out per day, and she asked her assistant

to use 25 days of data to construct the interval estimate, what confidence level can she attach

to the interval estimate?

a. 99.7%

b. 99.0%

c. 98.0%

d. 95.4%

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41

Which of the following is true regarding the sampling distribution of the mean for a large

sample size?

a. It has the same shape, mean, and standard deviation as the population.

b. It has a normal distribution with the same mean and standard deviation as the

population.

c. It has the same shape and mean as the population, but has a smaller standard

deviation.

d. It has a normal distribution with the same mean as the population but with a smaller

standard deviation.

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42

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab

conducts. Prices for 100 rats follow the following distribution:

Price:

$10.00 $12.50 $15.00

Probability: 0.35

0.40

0.25

How much should the lab budget for next year’s rat orders be, assuming this distribution does

not change?

a. $520

b. $637

c. $650

d. $780

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43

The portfolio expected return of two investments

a. will be higher when the covariance is zero.

b. will be higher when the covariance is negative.

c. will be higher when the covariance is positive.

d. does not depend on the covariance.

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44

According to a survey of American households, the probability that the residents own 2 cars if

annual household income is over $25,000 is 80%. Of the households surveyed, 60% had

incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household

do not own 2 cars and have an income over $25,000 a year is:

a. 0.12

b. 0.18

c. 0.22

d. 0.48

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45

Which of the following is most likely a parameter as opposed to a statistic?

a. The average score of the first five students completing an assignment.

b. The proportion of females registered to vote in a county.

c. The average height of people randomly selected from a database.

d. The proportion of trucks stopped yesterday that were cited for bad brakes.

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46

Which of the mean, median, mode, and geometric mean are resistant measures of central

tendency?

a. The mean and median only.

b. The median and mode only.

c. The mode and geometric mean only.

d. The mean and mode only.

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47

The collection and summarization of the socioeconomic and physical characteristics of the

employees of a particular firm is an example of

a. inferential statistics.

b. descriptive statistics.

c. a parameter.

d. a statistic.

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48

A population frame for a survey contains a listing of 6,179 names. Using a table of random

numbers, which of the following code numbers will appear on your list?

a. 06

b. 0694

c. 6946

d. 61790

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49

In left-skewed distributions, which of the following is the correct statement?

a. The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3.

b. The distance from the smallest observation to Q1 is larger than the distance from

Q3 to the largest observation.

c. The distance from the smallest observation to Q2 is smaller than the distance from

Q2 to the largest observation.

d. The distance from Q1 to Q3 is twice the distance from Q1 to Q2.

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50

Why is the Central Limit Theorem so important to the study of sampling distributions?

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a. It allows us to disregard the size of the sample selected when the population is not

normal.

b. It allows us to disregard the shape of the sampling distribution when the size of the

population is large.

c. It allows us to disregard the size of the population we are sampling from.

d. It allows us to disregard the shape of the population when n is large.

STAT125-HK. BUSINESS STATISTICS (STAT125-HK) > TAKE ASSESSMENT: FINAL EXAM

Question

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1

In testing for differences between the means of 2 independent populations, the null hypothesis

is:

a. H0: μ1 – μ2 = 2.

b. H0: μ1 – μ2 = 0.

c. H0: μ1 – μ2 > 0.

d. H0: μ1 – μ2 < 2.

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2

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches.

To test this claim against the alternative that the actual proportion of doctors who recommend

aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they

recommend aspirin. The value of the test statistic in this problem is approximately equal to:

a. -4.12

b. -2.33

c. -1.86

d. -0.07

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3

If a group of independent variables are not significant individually but are significant as a group

at a specified level of significance, this is most likely due to

a. autocorrelation.

b. the presence of dummy variables.

c. the absence of dummy variables.

d. collinearity.

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4

TABLE 13-2

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A candy bar manufacturer is interested in trying to estimate how sales are influenced by the

price of their product. To do this, the company randomly chooses 6 small cities and offers the

candy bar at different prices. Using candy bar sales as the dependent variable, the company

will conduct a simple linear regression on the data below:

City

Price

Sales

($)

River

1.30

100

1.60

90

Ellsworth 1.80

90

Prescott 2.00

40

Rock Elm 2.40

38

Stillwater 2.90

32

Falls

Hudson

Referring to Table 13-2, what is the coefficient of correlation for these data?

a. -0.8854

b. -0.7839

c. 0.7839

d. 0.8854

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5

The Y-intercept (b0) represents the

a. predicted value of Y when X = 0.

b. change in estimated average Y per unit change in X.

c. predicted value of Y.

d. variation around the sample regression line.

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6

TABLE 14-5

A microeconomist wants to determine how corporate sales are influenced by capital and wage

spending by companies. She proceeds to randomly select 26 large corporations and record

information in millions of dollars. The Microsoft Excel output below shows results of this μltiple

regression.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.830

R Square

0.689

Adjusted R

0.662

Square

Standard

17501.643

Error

Observations 26

ANOVA

df SS

MS

F

Signif F

Regression 2 15579777040 7789888520 25.432 0.0001

Residual

23 7045072780 306307512

Total

25 22624849820

Coeff

StdError

t Stat P-value

Intercept 15800.0000 6038.2999 2.617 0.0154

Capital

0.1245

0.2045

0.609 0.5485

Wages

7.0762

1.4729

4.804 0.0001

Referring to Table 14-5, what are the predicted sales (in millions of dollars) for a company

spending $100 million on capital and $100 million on wages?

a. 15,800.00

b. 16,520.07

c. 17,277.49

d. 20,455.98

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7

If we are performing a two-tailed test of whether μ = 100, the probability of detecting a shift of

the mean to 105 will be ________ the probability of detecting a shift of the mean to 110.

a. less than

b. greater than

c. equal to

d. not comparable to

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TABLE 11-1

Psychologists have found that people are generally reluctant to transmit bad news to their

peers. This phenomenon has been termed the "ΜM effect." To investigate the cause of the ΜM

effect, 40 undergraduates at Duke University participated in an experiment. Each subject was

asked to administer an IQ test to another student and then provide the test taker with his or her

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percentile score. Unknown to the subject, the test taker was a bogus student who was working

with the researchers. The experimenters manipulated two factors: subject visibility and

success of test taker, each at two levels. Subject visibility was either visible or not visible to

the test taker. Success of the test taker was either visible or not visible to the test taker.

Success of the test taker was either top 20% or bottom 20%. Ten subjects were randomly

assigned to each of the 2 x 2 = 4 experimental conditions, then the time (in seconds) between

the end of the test and the delivery of the percentile score from the subject to the test taker was

measured. (This variable is called the latency to feedback.) The data were subjected to

appropriate analyses with the following results.

Source

df SS

MS

F

PR >

F

Subject

1 1380.24

1380.24 4.26 0.043

Test taker 1 1325.16

1325.16 4.09 0.050

visibility

success

Interaction 1 3385.80

3385.80 10.45 0.002

Error

36 11,664.00 324.00

Total

39 17,755.20

Referring to Table 11-1, in the context of this study, interpret the statement: "Subject visibility

and test taker success interact."

a. The difference between the mean feedback time for visible and nonvisible subjects

depends on the success of the test taker.

b. The difference between the mean feedback time for test takers scoring in the top 20%

and bottom 20% depends on the visibility of the subject.

c. The relationship between feedback time and subject visibility depends on the success

of the test taker.

d. All of the above are correct interpretations.

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9

TABLE 13-1

A large national bank charges local companies for using their services. A bank official reported

the results of a regression analysis designed to predict the bank’s charges (Y) — measured in

dollars per month — for services rendered to local companies. One independent variable used

to predict service charge to a company is the company’s sales revenue (X) — measured in

millions of dollars. Data for 21 companies who use the bank’s services were used to fit the

model:

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E(Y) = β0 + β1X

The results of the simple linear regression are provided below.

Y = -2,700+20X, syx = 65, two-tailed p value = 0.034 (for testing β1)

Referring to Table 13-1, interpret the p…