Sample Exams - Aaec 3401

8/10/2019 Sample Exams - Aaec 3401

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4/32

MIN

$41,000

25%:

$88,000

MAX

$276,000

75"1,:

164,000

Construct

box

plot for the

data.

50,000

100,000

PROBLEMS.

Show all

of your

work.

No points

will be

giver-ror an

answer

without showing

horv

the answer

was

obtained.

Draw

diagrams

(with

labels or

the axes)

where appropriate

o

help explain

voLlransrvers.

Be

sure to

put

units

of

measurement

or

vour

answers.

Points or

each

question

are shown

in parentheses.

19)

(8

points) A random

sampleof

sale

pricesof homes

yielded

the following

summarv

information:

Median:

$130,000

+_+

150,000

200.000

250,000

300,000

350,000

400,000

Comment

on

a

home

that had a saleprice of $419,000.

A) The

saleprice wor-rld

e

expected ince t

falls nside

the ower

and

urpper ences.

B) This

value falls

outsicle lre

upper fence

and is considered

an outlier.

C) This value falls

outside

of the

third quartile,

but

cannotbe

considered

an outlier.

D)

This sale

price

falls

between

he ower

and

upper fences.

t

can be conside red

a

potential

outlier.

20)

(5

points)

A

survey oi 1877

American

households

ound

that

69%of the households

own

a computer.

clentifv

the

population,

he sample,

nd the ndividuals

n the

str.rdv.


5/32


6/32

22) (7 poit t ts) The r,r 'eishts

ir i

pror"rnds)

f 35

presclroolchildrerr are l isted bclon,

25 2a 26 26.\ 27 27 27.5 28 28 28.r

29

29.10 3L l i0 .5 i ] 31 32 32 .532 .1

33 33 3.1 3,t .5 35 35 37 37 i.q 38

40 42 13

.14.6

48

a) I j ind the first c1ualt i lr...how il oi

voul

r:alcul;rt ions.

b) F ind thc th i lc l

ouar t i l c .

S i ror . r ' i l o f

vour

ca lcu la t ions

c) Find the intertprart i lc larrge of t ire 35 n'eights l istecl rbtrve.

Siron' r,or-rLalcr-r lat jons


7/32

23) (-l0points)Listed

be'lor,r,re ire

AC'i 'scores

f 40 ranclon.rlv

elected

trrder.rtst a

n.rajor

-rniversitr

18 22 13 15 24 24 20 19

19 12

1 6 2 5 1 4 t 9 2 1 2 3 2 5 1 8

1 E 1 3

2 6

7 6 2 5 7 a 1 9 1 7 1 8 1 5

1 3 2 1

19 19 11 24 20 21 23 22 19 17

a) Constrr-rctireqnencv

listribrrt iorrableshou,ing

lass irnits

12-i3,

14*15,

. . ,26-27),reclr-tencv,

nd relative

irequenct,.

b) Constmct a rclat ir ' ' c 'rocluenc\,

n1 grlprh of the clata inclr-rde.rprpropnate

abels ancl a

t it ie)

c)

f the

universit l, ,\ 'antso .rccepthe top 90'X,

f

the

"rpplic.rnts,vhat

shor-rld

hc rninimum

score

e?

d) I f the

r-rniversitv

ets

he minimrlm

score at 18, vvirat

Lrercent

f the applicants vvil lbe

acceptecl?


8/32

24)

(8

points) T'lre

reigl 'r ts

in

inchcs)

rr i 6 adr-r ltmales

are l isted

belou.. Find thc- arlprlc variance

and standard

dcviat ion.

Shou' the

forr-nula(si -rse.d

nd all of

vour cil lci-r lat ior-rs.

65

73

r.4 bi

79 ;1


9/32

AAEC

340l ,Test#2

MWF

Name

SS#

Show

all of

vour

work for

the naffative

questions

nd

problems.

No

points

will be

given

or

an

answerwithout

showing how the answer

was obtained.

Draw diagrams

with

labels

or the

axes)

whereappropriate o help explain your answers. Be sure o put units of measurementor your

answers.Points or

each

question

are shown n

parentheses.

1.

(4 points)

a)

Draw

a scatter

lot

for the correlation

of Y and X where

: 0.10.

X

b) Drawa scatter

lot

or thecorrelation

f Y andX

where :

-0.94.

Y

Y

X


10/32

2.

(I0 points)

An

economistestimates regression

quation

o relate he

price

of a house o its

square ootage

area

of the heated

pace nside

he house). The data

used o estimate

he

equation

and the estimatedequation

are shown below.

Y=House rice

X=Square ootage

($1,000's)

80000

100000

125000

1

50000

11

0000

90000

a) What is the value

of the

Estimated

east-squares

egression

equation:

y

:18,790

+ 56.78x

1

100

1400

1500

2100

1

900

1

550

intercept

n the east-squares

egression

quation?

b) Can the intercept

be

interpreted

and explain

why or why not?

Interpret

he

ntercept

n oneor two

sentences.f that's

appropriate.

c) What is

the value of the slope n

the

east-squares

egression

quation?

Interpret he slope n

one or two sentences

Be

sure o

provide

a

precise

numericalexplanation

f

the

slope).


11/32

3.

(10

points)

The scores

n a testhaveamean

of

p:

100anda

standard eviation

f o: 15. If

a

personnel

manager

wishes o select rom

the top 75o/o

f applicantswho

take he test, ind

the

cutoff

score. Assume he variable

test

score) s normally

distributed.

Use a diagram

(with

labels) to il lustrate

your

answer.

4. (10 points)Theyield of a cottonvarietyhas a meanof p : 300poundsper acreand a standard

deviationof o: 90

poundsper

acre. What s

the

probability

hat he mean

yield

will be between

350 and

400

poundsper

acre? Assume he variable

test

score) s normally

distributed.

Use a

diagram

(with

labels)

o illustrate

your

answer.

5.

(10

points)

Consider

he

following

game

of chancewhere

a

player

rolls a

pair

of fair dice. If

the

player

olls2,

3,4, or 10, he

player

oses

5.

If the

player

olls5,

6, 8, 9,7I, or 12,

he

player

eceives

0

(i.e.,

eceives

othing). f

the

player

olls

a7,the

player

wins

$5.

a) Construct

a

probability

distribution

hat describeshe

game with

appropriate

eadings or

the

columns).

b) Compute he expected

alue of the

game

rom

the

player's point

of view. Show

he formula

usedand all

of

your

work.

6.

(6

points)

The data

below are or the

price

of a houseand he

square ootage

of the house.

Y=House

rice

($1,000's)

X=Square ootage

80000 11

00

100000

1400

125000

1500

150000

2100

'110000 '1900

90000 1550

The

correlationcoefficient

betweenhouse

price

and square ootage s

0.80. Calculate

he

coefficientof

determination. nterpret he

coefficientof determination

n one

or two sentences.


12/32

AAEC

3407,Test#2

TR

Name

SS#

Estimated

east-squaresegression

equation:

j ' =492+4.8x

Show

all of

your

work for

the narrative

questions

nd

problems.

No

points

will be

given

for an

answerwithout

showinghow the

answerwas

obtained. Draw

diagrams

with

labels

or the

axes)

whereappropriate o help explain your answers.Be sure o put units of measurementor your

answers.Points

or each

question

are shown n

parentheses.

1.

(6 points)

Y X

5 8

7 9

2 4

a) Use

he dataabove o

calculate r*y.

Show all of

your

calculations.

b) Use he dataabove

o calculate x2.

Show all of

your

calculations.

2.

(10 points)

An

agriculturaleconomist

estimates regression

quation

o relatecrop

yield

to

nitrogen

use. The dataused

o estimate he

equationand

he estimated quation

are shown

below.

Y=Yield

X=Nitrogen

Plot

(pounds/acre)

(pounds/acre)

1

z

?

4

1200

1

000

1400

1250

1350

1 5 0

125

200

140

170

a) What is the value

of the ntercept n

the east-squaresegression

quation?

b) Can the intercept

be

interpreted

and

explain why or why

not? Interpret

he intercept n

one or

two

sentences,f that's appropriate.

c)

What is the value of the

slope n the east-squares

egression

quation?

Interpret

he slope n

one or two sentences

Be

sure o

provide

a

precise

numerical

explanation

f

the slope).


13/32

_

3.

(10

points)

The

scores n atest haveamean

of

p:

i00 and

a standard eviation

f o: 12.

Find

the two limits

(x1

and x2)

that

nclude

he middle

50% of test scores.Assume

he variable

(test

score) s normally

distributed. Use a diagram

(with

labels) o illustrate

your

answer.

4.

(10 points)

The

yield

of a cottonvarietyhas

a meanof

p:310

pounds er

acre

anda standard

deviation

of o: 80

poundsper

acre. What

s the

probability

hat he meanyield will be above

375

poundsper

acre? Assume

he variable

test

score) s normally

distributed. Use a

diagram

(with

labels) o illustrate

your

answer.

5.

(8

points)

An Excel regression

utput s shown

below.

Y=HousePrice

X=Square

($1,000's)

Footaqe

11 0 0

1400

1

500

2100

1900

1

550

SUMMARY

OUTPUT

Regresslon

Sfafisfics

80000

1

00000

125000

150000

I 10000

90000

Mult iple

R Square

AdjustedR

Square

StandardError

Observations

0.80170942

0.642737995

0.553422493

16960.84738

h

ANOVA

df

SS

MS F

Siqnificance

F

Regression

Residual

Total

1

2070151958 2070151958

7.196265

0.05508

4 1150681376

287670343.9

5 3220833333

Coefficients

Standard

Error

f

Sfaf

P-value

Intercept

X=SquareFootage

18789.74692

34394.42715 0.546302075

0.613901

56.7813'1084 21.16663631

2.682585461

0.05508

Read he Excel regression

utput

(above)

o

answer he following

questions.

a) What is the correlationcoefficient?

b) What s the coefficient

of determination?

c) What s

the ntercept

b0)

in the east-squares

egression?

d) What is

the slope

b1)

in the east-squares

egression?


14/32


15/32

Test 2 Multiple Choice

MULTIPLE

CHOICE

(1.7

points each). Choose he one alternative that best completes he

statement or answers he question.

1) A die is rolled. The set of equally likely outcomes s

{1,

2,3,4,5,

6}.

Find the probability

of

getting

a 3.

A ) 3 D ) 0

2) For a standard normal curve, find the z-score

that separates he bottom 90% from the top 10%.

A) 0.28 B) 1.28

c) 7.52 D) 2.81

3) Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. t is known

that the amount of beer

poured by this filling machine follows

a

normal

distributi on with a mean of 12.37ounces and a standard

deviation of 0.04 ounce.

The

company

is interested

n reducing the amount of ex tra beer that is poured into

the

12

ounce bottles.

The

company

is

seeking o

identify

the highest 7.5% of the fill amounts poured

by this

machine.

For what fill amount are they searching?

A) 12.457 B) 11.913

c) 72.087 D) 12.283

B)+

o

q+

4)

In terms of probability, a(n)

A)

Sample space

-

is any processwith uncertain

C)Experiment

results

hat can be repeated.

D) Outcome

) Event


16/32

5) Given t he table of probabilities

for the random variable x,

does his form a

probability

distribution? Answer

Yes or No.

x

t.,

7 2

J

4

P(x)

0.02 0.07 0.22 0.27

0.42

A)Yes

B) No

A random

variable X is normally

distributed with

Fr

=

50.

Convert the

value

of X to

aZ-score,

if

the standard

deviation

is

as

given.

6 ) X : 6 3 ; o = 3

A ) 2 0

B ) 1

C ) 6 3

D ) 3

7) Find

the area under the standard normal

curve between z

=

0

and z

=

3.

A) 0.9987

B) 0.4641

C) 0.4987

D) 0.0010

8) A large national bank charges ocal companies or using its services.A bank official reported the results of a

regression

analysis designed to predict the bank's charges y),

measured n dollars per month,

for services

rendered

to local companies.One independent

variable used to predict

service charge o a company is

the

company's sales evenue

(x),

measured n millions

of dollars. Data for 21

companies who use the

bank's services

were used to fit the model

y:

l3O Prx.

The results

of the simple linear regressionare provided

below.

Y=2,700+20x

Interpret the estimate of

pg,

the

y-intercept of the line.

A) All companies

will be charged at least

$2,700

by the

bank.

B) About 95o/" f the observed

service charges al l withi n

$2,700

of the

least

squares ine.

C) For every

$1

million increase n

sales

evenue,

we expect a service

charge o increase

$2,700.

D) There is no practical interpretation

since a sales evenue

of

$0

s

a nonsensicalvalue.


17/32

9) The least

squares egression ine

A) Minimizes

the sum of the residuals

squared

B) Maximizes

the mean difference

between the residuals

squared

C) Maximizes the

sum of t he residuals squared

D) Minimizes

the mean difference

between the residuals

squared

10) The random

variable x represents he number

of tests hat

a

patient

entering a hospital

will have

along with the

corresponding probabilities.

Find

the

mean

and standard

deviation for t he random

variable x.

A) mean:

1.59;standard deviation:

3.72

C)

mean:

2.52: standard deviation:

1.93

11) Which o f the following cannot be a probability?

B) mean:

3.72; standard deviation: 2.52

D) mean: 1.59;

tandarddeviation:1.09

c ) 0

D) 0.001

E

A)Y

R \

-R5

12) High

temperatures n a certain

city

for

the month of August

follow a uniform

distribution over

the

interval

65'F

to

90'F. \zVhats the probability

that a randomly selected

August day has a high

temperature that

exceeded

70'F?

A) 0 . 8 B)

0.2

c )0 .04

D)

0.4516

13) A researcher

determines that the linear

correlation coefficient s

0.85 or a

paired

data

set.

This

indicates

that

there is

A) A strong positive linear correlation

B)

A strong negative linear

correlation

C) No

linear

correlation

but that there may be some

other relationship

D) Insufficient

evidence to make

any decision about

the correlation of the

data

14) The highest

point on the graph

of the normal density

curve

is

located at

x

l 0

1 l 2 l 3 l 4

5 l 6 l 2 l 1

1 7 l 1 7 l 7 7 l 7 7

A ) p r + o

B) An inflection

point C) Its mean

D )

p + 3 o


18/32

Make

a scatter

diagram

for

the

data. Use the

scatter diagram

to describe how, if

at all,

the

variables

are

related.

is)

Subject

x Time watching

TV

y

Time

on Internet

A)

r

6

6

9

1 1

B C D E

5 3 8

8

9 5 7 4 1 5

C

7

15

B)

D)

)

2 4

6 8 1 0 1 2 4 1 6 1 8 2 0

The variables

appear to

be

negatively,

linearly related.

2 4

6 8 1 0 1 2 1 4 1 6 1 8 2 0 x

The variables

do not

appear to be

linearly

related.

l 8

l 6

1 4

1 2

l 0

8

6

4

2

20

l 8

l 6

t 4

t 2

l 0

8

6

4

2

20

1 8

l 6

t 4

1 2

l 0

8

6

4

2

20

l 8

l 6

1 4

t 2

l 0

8

6

4

2

15

35

I O

9

6

4

2

I J

The

variables do not

appear to

be

linearly

related.

2 4 6

8

1 0 1 2 1 4 1 6 1 8 2 0 x

The

variables appear

to be

positively,

linearly related.

16) The table below representsa random sample of the number of deaths per 100cases or a certain llness over

time. If

a

person

infected

with this illness

s randomly

selected rom

all infected

people, find

the probability

that

the person

lives 3-4 years

after diagnosis.

Number deaths

1- 2

3-4

5-6

7-8

9-10

77-12

13-14

15+

7

A)

-- ;

0.058

I zU

? 5

B)

fr;

o'3s

? 6

C)

;0.s38

o3

D I;o.ozg

JJ

17) True

or False: The

area under

the normal

curve drawn

with regard

to the population

parameters

s the

same as

the proportion

of the population

that has these

characteristics.

2

4 6

I

t 0 1 2 1 4 1 6 1 8 2 0 x

A)

False

B) True


19/32

18) Find the area under the

standard normal curve betwe

en

z

=

7 and z

:

2

A) 0.5398 B)

0.1359

c) 0.8413

D) 0.213e

19) An instructor wishes

to determine if there is a relationship

between the number

of absences rom his

class and

a

student's final grade in

the course. What is the

predictor

variable?

A) Absences

C) The nstructor's oint scale or attendance

B) Student's performance

on the final

examination

D) Final Grade

20) If the coefficient

of determination is close to 1, then

A)

The linear correlation coefficient s

close o zero.

B) The least

squares egression ine

equation explains most of the

variation in the response

variable.

C) The least

squares

egression

ine equa tion has no

explanatory value.

D) The sum of the square residuals

s large compared to

the total variation.

21 )G i ven t heequa t i ono f a reg ress i on l i ne i sy=3* - l 0 , wha t is t hebes t p red i c t edva lue f o ryg i venx=2?

A) 16 B)

-5

C) 17

D)

-4


20/32

The

scatter diagram shows the relationship

between average number

of years

of education and

births

per

woman

of child

bearing age

n

selected countries.

Use the scatter

plot

to determine whether

the statement is

true or

false.

22)

Births per Woman

2 4 6 8 1 0 1 2 1 4

Average number

of

years

of education

of Married Women

of Child-Bearing Age

There is a

strong positive correlation

between years of education

and births per

woman.

A) False

B) True

probabilityof an outcome s

obtained y

dividing the requency

f occurrence

f an event

by the number of trials

of the experiment

A)Condi t ional

B)

Subjective

C) Classical

D)Empirical

24)

A physical fitness association s including

the mile run in

its secondary-school

itness test. The

time for this

event for boys in

secondary school s known

to possessa normal

distribution with

a

mean

of 450

secondsand a

standard

deviation of 60 seconds.Find

the

probability

that

a

randomlv

selected

bov in secondarv

school can run

the mile in l ess

han 312 seconds.

A) .e893 B) s107 c) .48e3

D) .0107

25)

Classify the following random

variable according to

whether it is discrete

or continuous.

The height

of a player on a basketball

team

A)

continuous

23)

The

B)

discrete


21/32

26) Is there a relationship

between the raisesadministrators

at StateUniversity receive

and their performance on

the iob?

A faculty group

wants to determine whether

job

rating

(x)

is a useful linear predictor

of raise

(y).

Consequently,

the group

considered he straight- line regress ion

model

i = p o * p r *

Using the method of least squares, the faculty group

obtained

the

following

prediction equation:

Y

:14,000

-

2,000x

Interpret the estimated

slope of the line.

A) For a 1-point increase n

an administrator's rating,

we estimate he administrator's

raise to decrease

$2,000.

B)

For a 1-point increase n

an administrator's rating,

we estimate he administrator's

raise to increase

$2,000.

C) For a

$1

ncrease n

an administrator's raise, we

estimate he administrator's

rating to decrease2,000

points.

D) For an administrator

with a rating of 1.0,we estimate his/her

raise o be

$2,000.

27)This

problem dea ls with eye

color, an

inherited

trait. For purposes

of this problem,

assume hat only two

eye

colors are possible,

brown and blue. We use b to represent

a blue eye gene

and B a brown eye gene.

f any B

genes

are

present,

the person will have

brown eyes. The table

shows the

four

possibilities for

the children of two

Bb

(brown-eyed)

parents,

where each parent has

one of each eye color gene.

SecondParent

B b

First

Parent B

b

Find the probability

that

A ) 0

theseparents give

birth

1

B ) -

+

to a child who has

blue eyes.

c ) 1

BB

Bb

Bb

bb

D)+


22/32


23/32

AAEC 3401, est#3

TR

Name

SS#

Show all of

vour

work

for

the narrative

questions

nd

problems.

No

points

will be

given

for

an

answer without showing how the

answer was obtained. Draw

diagrams

with

labels or

the axes)whereappropriateo helpexplainyour answers.Be sure o put units of measurement

for

your

answers.Points or each

question

are shown n

parentheses.

1.

(10 points)

A new variety

of

plums

was

developed nd est reeswere

planted

and

grown

to

produceplums.

The weight

of

plums

rom 6 treeswas measured

nd he sample

averageweight

of a

plum

is

shownbelow.

Tree Weight

ounces)

1

3 . 5

2 4 .0

a a -

J J . Z

4 3 . 9

s

3 . 6

6= 4.2

x . . . . . . . 3 . 7 5

s . . . . . . . . . 3 8

A commercial

rchardwould ike to determine hether

he new

plum

has

a highermeanweight

than

heestablished

currently

rown)plum

hathasa meanweight

of

p:3.25

ounces.

Carry out a test of the relevant null hypothesis

o determine

whether the mean weight

of the new

plum

is higher han

hat of the established

cunently

grown) plum.

Show all

4

stepsof test

of a

hypothesis, 1) null and alternative hypotheses; 2) critical value; (3) calculatedvalue; (4)

conclusion.Be sure o clearly number

your

steps.

Use he

*:r*Classical

Approach'(tr'

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Sample Exams - Aaec 3401

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