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Pace University

Fall 2020

MAT 117 CRN 70027

Instructor: Jing Chen

Exam 1

Date of Exam: Sep 23, 2020

MAT 117 (Fall 2020) Sample Exam 1

Name: __________________________________________________________

Important Instructions (please read):

1. This is a closed-book and closed-note exam. You are allowed to use the formula sheet

(provided by the instructor) and a calculator (scientific or graphing, prepared by student). No

other electronic devices or aiding tools are permitted.

2. Independent works are required and respected. Any suspicious behavior related to cheating

during the exam will be inspected. Cheating in the exam will result in an automatic zero score of

the exam and an instructor note to your affiliated department and college. Further investigation

and punishment will be handled by the University.

3. The exam is 1 hour 50 minutes. During the exam, a web clock will be projected on the screen

so you can check the time.

4. For True/False, provide your reasoning if your answer was false. For Multiple Choice, show

your reasoning or calculation. For Comprehensive Questions, show your steps and answers.

Correct answer alone without reasoning will not receive full credit. Partial credit will be given to

steps showing the right reasoning.

5. Write your solutions in the provided blank space below each question. If extra space is

needed, please request extra paper from the instructor during the exam.

True/False (4 points each)

1. A qualitative variable assumes meaningful numerical values.

2. All mathematical operations can be performed on ratio-scaled data.

3. A histogram is a series of rectangles where the width and height of each rectangle represent

the frequency (or relative frequency) and the width of the respective class.

4. The geometric mean is a multiplicative average of a data set used to measure values over a

period of time.

5. The variance and standard deviation are the most widely used measures of central location.

1

Pace University

Fall 2020

MAT 117 CRN 70027

Instructor: Jing Chen

Exam 1

Date of Exam: Sep 23, 2020

Multiple Choice (4 points each)

6. Which of the following represents a population and a sample from that population?

A) Attendees at a sporting event, and those who purchased popcorn at said sporting event.

B) Full-time employees at a marketing firm, and temporary summer interns at the marketing

firm.

C) Seniors at Boston College and students in a first-semester business statistics course.

D) Stocks available on the NYSE and stocks on the NASDAQ.

7. An undergraduate student’s status (freshman, sophomore, junior, or senior) is an example of

which scale of measurement?

A) Ratio scale.

B) Ordinal scale.

C) Interval scale.

D) Nominal scale.

8. Students in Professor Smith’s business statistics course have evaluated the overall

effectiveness of the professor’s instruction on a five-point scale, where a score of 1 indicates very

poor performance and a score of 5 indicates outstanding performance. The raw scores are

displayed in the accompanying table.

1

5

4

4

5

5

4

4

5

5

4

5

5

2

5

3

3

3

4

3

2

3

2

3

4

3

3

1

3

2

What is the relative frequency of the students who gave Professor Smith an evaluation of 3?

A) 0.3

B) 0.5

C) 9

D) 15

2

Pace University

Fall 2020

MAT 117 CRN 70027

Instructor: Jing Chen

Exam 1

Date of Exam: Sep 23, 2020

9. What type of relationship is indicated in the scatterplot?

A) No relationship

B) A negative linear relationship

C) A positive linear relationship

D) A positive curvilinear relationship

10. The accompanying relative frequency distribution represents the last year car sales for the

sales force at Kelly’s Mega Used Car Center.

Car Sales

35 up to 45

45 up to 55

55 up to 65

65 up to 75

75 up to 85

Relative Frequency

0.07

0.15

0.31

0.22

0.25

If Kelly’s employs 100 salespeople, how many of these salespeople have sold at least 65 cars in

the last year?

A) 22

B) 25

C) 31

D) 47

3

Pace University

Fall 2020

MAT 117 CRN 70027

Instructor: Jing Chen

Exam 1

Date of Exam: Sep 23, 2020

11. The following stem-and-leaf diagram shows the speeds in miles per hour (mph) of 14 cars

approaching a toll booth on a bridge in Oakland, California.

Stem

2

3

4

Leaf

56679

47789

0023

How many of the cars were traveling faster than 25 mph but slower than 40 mph?

A) 8

B) 9

C) 10

D) 12

12. The median defined as the ________.

A) middle point in a data set.

B) geometric average of a data set.

C) arithmetic average of a data set.

D) most common value in a data set.

4

Pace University

Fall 2020

MAT 117 CRN 70027

Instructor: Jing Chen

Exam 1

Date of Exam: Sep 23, 2020

Comprehensive Questions

The following data represent a sample of non-elementary mathematics teachers in Bergen

County, New Jersey. Answer the following questions.

Masters

Masters

Years’

Experience

8

25

$67,945

$82,910

Classes

Taught

6

4

Bachelors

25

$86,030

7

Bachelors

3

$62,690

5

Masters

21

$82,620

5

Masters

Masters

Masters

Masters

Masters

11

41

31

10

3

$82,330

$79,790

$82,626

$82,626

$98,291

5

4

5

4

4

School

Degree

Brookside E.S.

Program 3-Emothionally

Distur.

Program 3-Emothionally

Distur.

Program 3-Emothionally

Distur.

Program 3-Emothionally

Distur.

Program 5-Life Skills

Program 5-Life Skills

Bergen Academies-Hackensack

Bergen Academies-Hackensack

Bergen Academies-Hackensack

Salary

Source:

http://php.app.com/edstaff/results2.php?county=BERGEN&district=%25&school=%25&lname=

&fname=&job1=Math+Non-Elementary&Submit=Submit

13 (4 points). Identity the two variables with ratio scale of measurement.

14 (4 points). Is “Degree” a qualitative or a quantitative variable? Explain.

15 (5 points). List all categories in the “School” variable.

16 (8 points). Build a frequency distribution table for the “Salary” variable.

17 (8 points). Construct a histogram for the “Salary” variable.

18 (3 points). How many percent of teachers taught less than 6 classes?

5

Pace University

Fall 2020

MAT 117 CRN 70027

Instructor: Jing Chen

Exam 1

Date of Exam: Sep 23, 2020

The Yearly Prices (rounded to the nearest dollar) for GLD (a gold exchange traded fund, denoted

as x) and SLV (a silver exchange traded fund, denoted as y) are reported in the following table.

Year

1

2

3

4

5

GLD

38%

5%

26%

26%

12%

SLV

25%

–27%

55%

76%

–4%

19 (8 points). Calculate the sample variance and sample standard deviation for the GLD and

SLV.

20 (2 points). Which asset had a higher risk?

21 (4 points). Which asset had the greater relative dispersion?

22 (6 points). Describe the relationship between the two funds using the correlation coefficient.

6

M 117 Elementary Statistics Formula Sheet

Binomial probability of x successes in n

trials: 𝑃(𝑥) = 𝑛𝐶𝑥 𝑝 𝑥 (1 − 𝑝)𝑛−𝑥

2

Coefficient of determination: 𝑟 =

∑(𝑦̂−𝑦̅)2

∑(𝑦−𝑦̅)2

𝑠

Mean of a frequency distribution: 𝑥̅ =

∑(𝑚⋅𝑓)

𝑛

Mean (expected value) of a discrete

random variable: 𝜇 = ∑ 𝑥𝑃(𝑥)

Coefficient of variation: 𝐶𝑉 = 𝑥̅

Minimum sample size to estimate 𝝁: 𝑛 =

Combination of n objects taking x: 𝑛𝐶𝑥 =

(

𝑛!

(𝑛−𝑥)!𝑥!

𝑧𝑐 𝜎 2

)

𝐸

Minimum sample size to estimate 𝒑: 𝑛 =

𝑧

2

Confidence interval for a mean: 𝑥̅ − 𝐸 <
𝜎
𝑠
𝜇 < 𝑥̅ + 𝐸, where 𝐸 = 𝑧𝑐 𝑛 or 𝐸 = 𝑡𝑐,𝑑𝑓 𝑛
𝑝̅ (1 − 𝑝̅ ) ( 𝐸𝑐 )
Confidence interval for a proportion: 𝑝̅ −
𝑛!
(𝑛−𝑥)!
√
√
𝐸 < 𝑝 < 𝑝̅ + 𝐸, where 𝐸 = 𝑧𝑐 √
𝑝̅ (1−𝑝̅ )
𝑛
Confidence interval for a variance:
(𝑛−1)𝑠2
2
𝜒𝑅
< 𝜎2 <
(𝑛−1)𝑠2
𝜒𝐿2
Confidence interval for a standard
(𝑛−1)𝑠2
deviation: √
2
𝜒𝑅
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attachment
Tags:
correlation coefficient
numerical data
Sample Variance
Relative dispersion
standard deviation
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