spring 12 econ-e370 iu exam 1 review

8/2/2019 Spring 12 ECON-E370 IU Exam 1 Review

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ECONE370 Exam 1 Review

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Summarizing Data

1. In a recent survey of 100 IU students, it was found that 60% of them have seasontickets to all home IU basketball games. However, the database at the IU ticket

office indicates that 62.3% of IU students have season tickets to all home IU

basketball games. The values of 60% and 62.3% are

(A) a statistic and parameter, respectively

(B) a parameter and statistic, respectively

(C) both statistics

(D) both parameters

The value of 60% is a_________________ because it comes fromthe ____________________

The value of 62.3% is a_________________ because it comes fromthe ____________________

2. Which of the following variables are qualitative?I. An IU students gender

II. An IU students GPA

III. An IU students social security number

(A) I only

(B) I and II only

(C) I and III only

(D) II and III only

(E) I, II, and III


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3. Which of the following variables are discrete quantitative?I. The number of times an IU student gets high each day

II. The number of bongs present in an IU students dorm room

III. The number of ounces in a can of beer

(A) I only

(B) I and II only

(C) I and III only

(D) II and III only

(E) I, II, and III

4. Which of the following variables are continuous quantitative?

I. The amount of time spent drinking by an IU studentII. The number of bars an IU student visits in one night

III. An IU students height

(A) I only

(B) I and II only

(C) I and III only

(D) II and III only

(E) I, II, and III

5. Suppose that you intend to take a cruise for Spring Break. Identify each of thefollowing as either an ordinal or nominal variable (or neither).

P. The cruise line you selected (e.g. Carnival, Royal Caribbean, etc)

Q. The class of cabin purchased on a cruise ship (e.g. interior,

balcony, suite, etc)

R. The credit card number you used to book the cruise

S. The size of the ship you selected (in tonnage)

Nominal Ordinal(A) P and Q R and S

(B) P and R Q

(C) P and R Q and S

(D) Q and R P

(E) None of the above


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Sampling Methods

6. Which of the following is NOT true of a stratified random sample?(A) Randomization is employed within the sampling procedure

(B) The population is divided into groups of units that are similar in somerespect

(C) The division of items into strata is done so based upon information obtained

prior to sample selection

(D) Each individual in the population can belong to multiple strata

7. The manager of a local Best Buy wants to estimate the mean battery life of allremote controls in a shipment of remote controls from a supplier. The shipment

consists of 40 boxes each containing 25 remote controls. The manager lists all

boxes from 140 and randomly selects 6 boxes determines the battery life of allremote controls within the boxes selected. What type of sampling is being used?

(A) simple random sample

(B) systematic sampling

(C) stratified sampling

(D) convenience sample

8. A statistician is attempting to gather a systematic random sample of n = 20football coaches for all BCS division I teams (e.g. Indiana, Ohio State, Florida,etc). All 360 such coaches have been identified, sorted by school and numbered

from 1 to 360 in alphabetical order based first upon the state in which they reside

(e.g. Alabama) and then, within each state, by the name of the school itself (e.g.

Alabama, Auburn, etc). The first school in this sequence is assigned as number 1.

The statistician wishes to estimate the mean number of wins per season for these

coaches. The 266th of all coaches was selected as the fourth observation in the

sample. What is the number of the first observation in the sample?

(A) 200th

(B) 212th

(C) 230th

(D) More information is needed to answer this question

k =N

n=

360

20

= 18


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Summary Statistics Exercise

Suppose a group of IU students is asked how many nights per week they go out

drinking. The results are shown below.

4 2 5 3 4 5 7 8

(a) Determine the mean for these values assuming these students represent (i) a

random sample and (ii) the entire population.

sample mean population mean

x=

x

i=1

n

!n

=4 + 2 + ... + 8

8

=38

8

= 4.75 =x

i=1

n

!N

=4 + 2 + ... + 8

8

=38

8

= 4.75

(b) Determine the median for these data.

First, lets order these values

2 3 4 4 5 5 7 8

sample median = M = 4 + 52

= 4.5

(c) Determine the sample range.

sample range = Max Min = 8 2 = 6


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4 2 5 3 4 5 7 8

(d) Determine the variance for these values assuming these students represent (i) a

random sample and (ii) the entire population.

sample variance:

s2=

(x! x)2

i=1

n

"

n! 1=

(4 ! 4.75)2 + (2 ! 4.75)2 + ... + (8 ! 4.75)2

8 ! 1=

27.5

7= 3.929

population variance:

!2=

(x" )2

i=1

n

#

N=

(4 " 4.75)2 + (2 " 4.75)2 + ... + (8 " 4.75)2

8=

27.5

8= 3.4375

(e) Determine the standard deviation for these values assuming these students

represent (i) a random sample and (ii) the entire population.

sample SD population SD

s= s2= 3.929= 1.98 ! = !2 = 3.4375 = 1.85


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4 2 5 3 4 5 7 8

(f) Determine the interquartile range for these data values.

First, lets order these values

2 3 4 4 5 5 7 8

Recall:Lp

= (n+ 1)p

100

Q1L25 = (8 + 1)25

100= 9(.25) = 2.25

lower + (decimal)(upper ! lower) =

Q3L75 = (8 + 1)75

100= 9(.75) = 6.75


IQR = Q3 Q1 =


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TI83/84 Instructions for finding summary statistics

Step #1: Press the STAT key,

and press ENTER while on

Option #1 of EDIT.

Step #2: Enter data values into

L1. If there is already data in

L1, arrow up until L1 is

highlighted, press CLEAR andarrow back down.

Step #3: Press the STAT key,

arrow over to CALC and press

ENTER while on Option #1.

Step #4: If you have your datain L1, just press ENTER.

Otherwise, specify the list, e.g.

press 2nd 2 for L2, and press

ENTER.

Step #5: Youre done!x = 4.75 & s = 1.98.

[Ignore ]

If you arrow down, youll findthe 5 number summary.

However, we CANNOT use

the given values of Q1 and Q3

We can see that: sample mean = x = 4.75 (which is the same as the population mean), sample

standard deviation = s = 1.982, & population standard deviation = = 1.85

To find the sample variance, just square s, i.e. s2 = (1.982)2 = 3.928 times2.

[Dont forget when reporting the variance that the variance is in SQUARED units.]

Note:

If you accidentally deleted one or more of your lists by

pressing DEL instead of CLEAR, to get your lists back, pressthe STAT key and press ENTER will on Option #5 of EDIT,

i.e. SetUpEditor. You should now have your lists back.


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Summary Statistics

9. Suppose a stockbroker is deciding between investing the same amount of moneyin either stock A or stock B. He estimates that the mean and standard deviation

for the returns resulting from the investment in stock A are $100 and $30,

respectively. The mean and standard deviation for the returns resulting from theinvestment in stock B are $500 and $100, respectively. Which stock is riskier?

(A) Stock A

(B) Stock B

(C) Stocks A and B exhibit the same amount of riskiness

(D) It is impossible to determine which stock is riskier without knowing the

medians return for each stock

CVA=

s

x! 100% CVB =s

x! 100%10. At a local ChickfilA, the mean amount of money spent per order (in one day) is

determined to be $12.50 with a standard deviation of $2. Within this same day, a

person is standing in line waiting to order a chicken/waffle fry goodness. The

standard deviation will increase the most if the order is for _________ and it will

decrease the most if the order is for _________.

(A) $0; $0

(B) $30; $12.50

(C) $0; $12.50

(D) $30; $0

11. A sample of 10 observations has a variance of 16. The sum of squared deviationsfrom the mean is

(A) 160

(B) 144

(C) 40(D) 36

s2=

(x! x)2

"n! 1


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Use the following information for the nextFOUR questions.

A large travel agency is interested in the price and length of various cruises that

depart from Miami, Florida. To this end, she randomly samples several

departures and determines the pretax price of the cruise (in dollars) as well as

the duration of the cruise (in days). The following Excel output is generated forthe aforementioned sample.

Price Duration

Mean 608.73 Mean

Median 592.54 Median 5.29

Standard Deviation 157.62 Standard Deviation

Sample Variance Sample Variance 4.65

Minimum 299.00 Minimum

Maximum 1249.00 Maximum

Sum Sum 200.00

Count Count 32

12. If an adventurous individual insisted upon going on all of the cruises sampled,what would be the approximate pretax price he/she would have to pay?

(A) $17,210

(B) $19,480

(C) $15,690

(D) Excel is needed to answer this question

13. The mean duration for the first 30 cruises sampled was 6.10 days. What was themean duration for the remaining cruises sampled?

(A) 8.2 days

(B) 8.5 days

(C) 7.6 days(D) Excel is needed to answer this question

sum of last 2 cruises = 200 (30)(6.10) = 17


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Price Duration

Mean 608.73 Mean 6.25Median 632.17 Median 5.29

Standard Deviation 157.62 Standard Deviation 2.16Sample Variance 24844.06 Sample Variance 4.65Minimum 299.00 Minimum ???Maximum 1249.00 Maximum ???Sum 19479.36 Sum 200.00Count 32 Count 32

14. On which characteristic are these cruises the least symmetrical, price or duration?(A) Price

(B) Duration

(C) The symmetry for price and duration are identical


Symmetry measured by Pearsons 2ndSkewedness Coefficient

For Price 3(x! median)

s

For Duration3(x! median)

s

15. Suppose that we considered all of these cruises to represent the entire populationof all such cruises. What would be the variance for the durations?

(A) less than 4.65

(B) equal to 4.65

(C) greater than 4.65

(D) Cannot be determined solely by this information


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Use the following information for the next TWO questions

A random sample of IU students is taken and each student is asked to report

how many hours per week they spend Facebook stalking. The data are

summarized in the table below.

Number of hours Number of students

14 35

57 30

89 22

1012 13

16. What are our estimates for the mean, median, and mode for this data set?(A) mean 5.975, median 6, mode 2.5

(B) mean 6, median 5.975, mode 2.5(C) mean 5.975, median 6, mode 6

(D) mean 6.25, median 6.5, mode 2.5

meanxest

=

Mif

i!

fi

!

medianL50

= (100 + 1)50

100

17. Assume that the estimated mean of this data set is 7. What is our estimate for thevariance of this data set (rounded to two decimal places)?

(A) 9.27

(B) 9.96

(C) 10.06

(D) None of the above is/are correct

variance sest

2=

fi(M

i! x

est)2

"n! 1


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Graphical Displays Exercise

Suppose a random sample of 12 Purdue students is asked the question What is three

plus five? Their responses are shown below (as an ordered array).

1 1 4 4 8 9 9 9 10 10

Note: Two students did not respond but instead began crying uncontrollably. They were

removed from the sample.

(a) Create a frequency distribution for the responses.

Response f

1

4

89

10

(b) Create a relative frequency distribution for the responses.

Response Relative Frequency

1

4

89

10

(c) Create a cumulative frequency and cumulative relative frequency distribution

for the responses.

Response Cum. Frequency Cum. Rel. Freq.

1

48

9

10


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Graphical Displays

18. An Kazakhstanbased airline is attempting to determine what most of theircustomer complaints reference in an effort to improve the overall quality of air

travel on their airline. They noted that the two most common complaints (as a

percentage of overall complaints) were relating to the smell of the aircraft andthe presence of livestock on board the aircraft. Which of the following displays

would be the most appropriate and informative display for these data?

(A) ogive

(B) pie chart

(C) histogram

(D) Pareto diagram

19. A recent study attempted to discern the level of douchebaggery at three Big 10schools. For the most recent school year, Ohio State admitted 3,000 douche bags,

Michigan admitted 4,200 douche bags, and Purdue admitted 39,726 douche bags

(their entire student body!). Which of the following displays would be the most

appropriate and informative display for these data?

(A) ogive

(B) pie chart(C) histogram

(D) Pareto diagram

20. Which of the following statements regarding qualitative displays is FALSE?(A) The choice of utilizing a bar chart vs. a pie chart is subjective

(B) A bar chart can be used for ordinal data

(C) Pareto diagrams are organized left to right from smallest frequency to largest

frequency

(D) It is inappropriate to use a Pareto diagram for interval data because interval

data already have an inherent order


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21. The following is a histogram showing the opening prices on the exchange of aparticular stock for 50 randomly selected days (rounded to the nearest $10).

Based on the frequency histogram for the NASDAQ, the 80th percentile is closest

to which of the following values?

(A) $20(B) $30

(C) $40

(D) $50

Stock Prices

Frequency

100908070605040302010

16

14

12

10

8

6

4

2

0

Histogram of Stock Prices

22. After the Florida Gators beat Ohio State twice for a National Championship,many residents immediately spent money on antiOSU paraphernalia. A sample

of n = 30 UF students was each asked how much money they had spent on their

most recent purchase of said items. The data was used to construct the

cumulative frequency plot shown below.

Which of the following statements regarding this display is TRUE?

(A) The median for this data set is approximately $60

(B) The IQR for this data set cannot be approximated by this display alone

(C) The mean for this data set can be approximated by this display alone

(D) There were no observations in this data set between $80 and $90

0

20

40

60

80

100

20 30 40 50 60 70 80 90 100

Amount ($)

CumulativeRelativ

e

Frequency


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Use the following information for the next TWO questions

The Pug Factory turns regular dogs into

fantastically smushyfaced pugs (illustration is to

the right). However, there is variation in the

process. In order to understand this variation, arandom sample of observations is taken where

the amount of time required to adequately smush

the dogs face (in seconds) is recorded. The

following stem and leaf diagram resulted.

0 3 6 2 5 1

1 2 8 5

2 6 4 1 1

3 0

4 6 9

23. What is the 80th percentile of these observations?(A) 13.0

(B) 25.6

(C) 29.2

(D) 30.0

L80

= (15 + 1)80

100= 16(.80) = 12.8


24. Suppose that this data set were to be transformed into a frequency distribution inwhich the classes were 10 seconds wide. What would be the upper bound of thethird class?

(A) 29

(B) 29.9

(C) 30

(D) 19.9


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Chebychevs Theorem and the Empirical Rule

Use the following information for the nextFOUR questions

Suppose the amount of money spent getting shwasted on a typical Saturday

night by all IU students has a mean of $30 and a true standard deviation of$5.

25. Assume that the distribution of observations is approximately normal.According to the Empirical Rule, what percent of observations should fall

between $20 and $40?

(A) 68%

(B) 95%

(C) 99.7%

(D) 16%(E) None of the above

How many standard deviations above/below mean?

# SDs above = 40 ! 305

# SDs below = 30 ! 205

26. Assume that the distribution of observations is bellshaped and symmetrical. Ifthere are 40,000 students at IU, how many of these students (to the nearest whole

number) does the Empirical Rue predict will spend between $25 and $45 getting

shwasted?

(A) 33,540

(B) 20,000

(C) 19,940

(D) 38,000

(E) This quantity cannot be determined exactly

How many standard deviations above/below mean?

# SDs above = 45 ! 305

# SDs below = 25 ! 205


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27. According to Chebychevs Theorem, what percent of observations should fallwithin 4 standard deviations of the mean?

(A) approximately 89%

(B) approximately 97%

(C) at least 89%(D) at least 93.75%

(E) at least 96%

At least 1 !1

k2

"

#$

%

&'%=

28. Chebychevs Theorem suggests that at least 60% of students will spend howmuch money getting shwasted (to the nearest dollar)?

(A) between $20 and $40

(B) between $25 and $35

(C) between $19 and $46

(D) between $18 and $43

(E) between $22 and $38

k =1

1 ! p

Now, lets go up/down that many SDs from the mean

$30 + ____________ ($5) =

$30 ____________ ($5) =


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Covariance and Correlation

Use the following information for the next THREE questions

A statistician random sample of IU students playing Sink the Biz at Nicks and

each is given the following threequestion survey:

How many times in the past month have you played Sink the Biz? _____________ How many minutes have you been sitting here playing Sink the Biz? _____________ How many fingers am I holding up? _____________

The following covariance matrix is computed in Excel.

Times/Month Minutes Fingers

Times/Month 31.695Minutes 95.364 448.495

Fingers 1.062 10.209 3.695

29. As per the covariance matrix, the covariance between the first and thirdresponses is 1.062 timesfingers. Which of the following is a correct statement

regarding this value?

(A) Generally, those students who play Sink the Biz more often per month saw

more fingers and the relationship is quite strong.

(B) Generally, those students who play Sink the Biz more often per month sawmore fingers and the relationship is quite weak.

(C) Generally, those students who play Sink the Biz more often per month saw

fewer fingers, though we cant comment as to the strength of the relationship.

(D) Generally, those students who play Sink the Biz more often per month saw

more fingers, though we cant comment as to the strength of the relationship.

30. The researchers realized that although only 3 fingers were actually being heldup, nearly all responses were well above 5 implying that the participants were so

drunk, they were seeing double. Therefore, the researcher took all responses to

this question and cut them in half. After this alteration, the covariance between

minutes and fingers will be

(A) 10.209

(B) 10.209

(C) 5.105

(D) 5.105


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Times/Month Minutes Fingers

Times/Month 31.695

Minutes 95.364 448.495

Fingers 1.062 10.209 3.695

31. Between which pairs of variables is the linear relationship the strongest?(A) Times/month and minutes

(B) Times/month and fingers

(C) Minutes and Fingers


In order to determine the strength/direction of the relationship,

we need to get the correlations, not covariances.

Lets start off by getting the standard deviation for each variable

Times/Month SD = 31.695 = 5.629

Minutes SD = 448.495 = 21.178

Fingers SD = 3.695 = 1.922

Now, lets get the correlation for each pair of variables using

r=s

XY

sX! s

Y

Times/month and minutes r =

Times/month and fingers r =

Minutes and Fingers r =


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Linear Regression


Ten IU guys were randomly selected at a local bar and each was asked how

many beers they had consumed and how many of the women in the bar lookedgood to them. The following information resulted from the analysis:

r = .698 women = 22.316 + 2.508(beers)

32. To the nearest whole number, how many women are predicted to look good to aguy who consumes 5 beers?

(A) 32

(B) 33(C) 35

(D) 39

x = 5 22.316 + 2.508(5) =

33. Suppose an individual in this sample drank 8 beers and thought that 40 womenin the bar looked good. How much (to the nearest whole number) did this

individual contribute to the sum of squared errors?

(A) 2

(B) 4

(C) 6

(D) 12

x = 8 22.316 + 2.508(8) =

error = y y =

SSE = (Y ! Y ')2"


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r = .698 women = 22.316 + 2.508(beers)

34. Which of the following statements is FALSE regarding this model?(A) This model predicts that for each additional 2 beers consumed, approximately 5more women are predicted to look good.

(B) This model predicts that before a guy consumes any beers, about 22 of the

women in a bar are predicted to look good.

(C) Supposing there were 500 women in the bar at the time this survey took

place, if the data values were gathered as the percent of women in the bar who

look good as compared to the number who look good, the correlation between

these variables would no longer be r = .698

(D) The covariance between number of women and number of beers could have

been 225.6 beerwomen.

35. The regression line for these data was given earlier as women = 22.316 +2.508(beers). Which of the following is true regarding this line?

(A) This is the line (of all possible lines) that passes though the largest number of

actual data points.

(B) This is the line (of all possible lines) that minimizes the sum of the vertical

distances between the actual values and those values predicted by the regression

line.

(C) This is the line (of all possible lines) that minimizes the square of the sum of

the vertical distances between the actual values and those values predicted by

the regression line.

(D) This is the line (of all possible lines) that minimizes the sum of the squared

vertical distances between the actual values and those values predicted by the

regression line.


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23

Probability Rules


Suppose we are interested in the association between the school a student goes to

and the gang he/she is in. The data from random sample of students is shownbelow in this two-way contingency table.

Gang TOTAL

School Tree Trail Eastside Boys Da Woods

Eastside 10 5 40

Santa Fe

Buchholz 20 25 60

TOTAL 40 55 200

36. What is the probability that a randomly selected student either went to Santa FeHigh School or was in Da Woods?

(A) .225

(B) .775

(C) .750

(D) .025

P(A or B) = P(A) + P(B) P(A and B)

37. If we know a student did NOT attend Buchholz High School, what is theprobability that they were NOT in Tree Trail?

(A) .821

(B) .179

(C) .659(D) None of the above answers is/are correct


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Gang TOTAL

School Tree Trail Eastside Boys Da Woods

Eastside 10 5 25 40

Santa Fe 15 80 5 100

Buchholz 15 2025 60

TOTAL 40 105 55 200

38. Among the choices below, which of the following is least likely to occur?(A) A randomly selected student is in Da Woods and attends Buchholz.

(B) A randomly selected student attending Santa Fe High School is in Tree Trail.

(C) A randomly selected student in Tree Trail attends Santa Fe High School

(D) A randomly selected student attends Buchholz High School

39. If gang and school are, in fact, independent, how many students should weexpect to see in the greyed cell?

(A) 15

(B) 20

(C) 25

(D) 30

expected =row total ! column total

grand total=


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Discrete Random Variables

Use the following information for the nextFIVE questions

Barney Stinson is looking to insure his $10,000 diamond suit. An insurance

company has determined the following distribution for the percentage of valuelost on the value of such a legend wait for it dary suit.

Percent Loss Probability of Loss

Total Loss 0.02

50% loss 0.03

25% loss 0.15

40. From the perspective of the insurance company, what is the expected loss?(A) $0

(B) $725

(C) $2,500

(D) $5,000

E(X) = = X! P(X)"#$%&

41. What premium should the insurance company charge Barney if they wish tomake an expected profit of $200 per policy?(A) $525

(B) $925

(C) $1,025

(D) Excel is needed to answer

42. Again, from the perspective of the insurance company, what is the value of themedian expected loss?

(A) $0

(B) $725

(C) $10,000



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Loss Percent Loss Probability of Loss$10,000 Total Loss 0.02$5,000 50% loss 0.03

$2,500 25% loss 0.15$0 0% loss .80

43. What is the shape of this probability distribution?(A) Strongly positively skewed

(B) Strongly negatively skewed

(C) Slightly positively skewed

(D) Slightly negative skewed

44. Assume that the insurance companys expected loss is $1,200. What is expectedthe standard deviation of the loss (to the nearest $10)?

(A) $350

(B) $2,420

(C) $3,100

(D) $3,710

!2= (X" )2 # P(X)$%

&'( ! = (X" )

2 # P(X)$%&'(


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Random Variable Transformations

45. A large data set has a mean of 100 and a variance of 20. If each data value isdivided by 2, the new mean and variance of the data set are

(A) 50 and 10, respectively(B) 50 and 5, respectively

(C) 100 and 10, respectively

(D) 100 and 5, respectively

46. A professor at a large university is instituting a curve by applying atransformation to all students current score on a recent exam. The

transformation is as follows:

Curved Score = 2.5(current score) + 10

Which of the following is NOT true?

(A) The mean of the curved scores is 2.5(the mean of the current scores) + 10

(B) The standard deviation of the curved scores is 2.5(the standard deviation ofthe current scores)

(C) The variance of the curved scores is 2.5(the variance of the current scores)

(D) None of the above. That is, all of the above are true.

spring 12 econ-e370 iu exam 1 review

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