Explain how random events behave in the short run and in the long run


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Review and Exercitation Exam Questions for Exam 2
Learning Objectives:
Chapter 17: Thinking encircling luck




Explain how purposeless smoothts beaccept in the brief run and in the hanker run and how purposeless and
haphazard are not the corresponding gist.
Perform basic presumption calculations using die flattens and fabricate tosses.
Define presumption, and use the rules for presumption.
Explain whether the law of mediocres is gentleman.
Explain how specific presumption differs from a philosophical or tentative presumption.

Chapter 18: Presumption copys



Define a presumption copy. Cause a presumption copy for a detail recital’s smoothts.
Apply the basic rules of presumption to a recital gist.
Calculate probabilities using a presumption copy, including summing up probabilities or
subtracting probabilities from the sum.
Define a sampling classification.

Chapter 20: The offspring edge: expected esteems


Define expected esteem, and reckon the expected esteem when absorbed a presumption copy.
Define the law of comprehensive entirety, and teach how it is opposed from the fabulous “law of
averages.”
Explain how casinos and prophylactic companies forthcoming in occupation and ascertain specie.

Chapter 13: The Normal classification






Identify postulates that is Normally exclusive.
Discuss how the shape/position of the Normal deflexion substitutes when the test rupture
increases/decreases or when the mediocre increases/decreases.
Define the testized esteem or Z-score. Reckon the Z-score, and use the Z-acenumerate to do
comparisons.
Calculate probabilities and cut-off esteems using the 68%-95%-99.7% (Empirical) Rule.
Identify the mediocre, test rupture, cut-off esteem, presumption, and Z-acenumerate on a Normal deflexion.
Use the Normal board to get percentiles (probabilities) for self-assertive gists and to get Z-scores
in enjoin to determine cut-offs for awkward gists using twain > and < in the inequalities.
Recognize whether a recital is a self-assertive or awkward Normal classification gist, and perform
the alienate calculations professioning set-just notation, the judicious presumption indication, and all
needful steps.

1

Chapter 21: What is a assurance intermission?







Define statistical corollary and teach when statistical corollary is used.
Explain what the assurance intermission mediocres and whether the results sharp-end to the population or
the scantling.
Calculate the brink of fallacy and identify the brink of fallacy in a assurance propoundment.
Explain what pattern of fallacy is familiar in the brink of fallacy.
Determine whether a recital is meliorate forcible forthcoming a while a rate or a mediocre.
Use alienate notation for rates and mediocres, twain in the population and the scantling.
Calculate a assurance intermission for a rate and for a mediocre.
Describe how increasing/decreasing the scantling extent or assurance equalize substitutes the brink of
fallacy (width of the assurance intermission).
Apply calculating for using assurance intermissions.
o Need a pure purposeless scantling.
o Postulates must be placid set-rightly.
o No outliers.

2

Practice Exam Questions
These exercitation exam investigations are not mediocret to be an consumptive flatten. These are solely examples of
questions that accept been asked in the spent. You definitely should try agoing through these examples
forthcoming a while your swindle shuffle, but ascertain believing that you use the Learning Objectives to cause your swindle shuffle
and to aid you ascertain other gists to exercitation. Your schoolmaster uses the Learning Objectives when
writing the exams. The odd-numbered gists in your capacity accept rejoinders in the tail, and the
StatsPortal website has numerous vast media to aid your con-overing, chiefly the Learning Curve
quizzes and the video order. Remember that you are undisputed to produce a 1-page (twain verges ok),
handwritten-in-your-own-handwriting, 8 ½” x 11” swindle shuffle forthcoming a while you to the exam. Your indicate should
be on the swindle shuffle, and it succeed be excellence 1 sharp-end on the exam when you exist it in.
The exemplification/sampling artifice and ethics topics from Exam 1 are great throughout the perfect
semester and may profession up on forthcoming exams.
1. Before the 2008 presidential belligerence, the Gallup Poll asked a scantling of 1,000 fellow-creatures for
whom they would signification for president; 52% said Obama. The brink of fallacy for a 95%
assurance intermission propoundd by counsel reports of this poll was:
A) ±8%

B) ±6%

C) ±4%

D) ±3%

E) ±2%

Show your production:

2. “Margin of fallacy” in this predicament mediocres that if tclose is no bias
A)
B)
C)
D)
E)

every scantling the Gallup Poll takes succeed forthcoming at smallest this seal to the faithfulness.
encircling half of the scantlings the Gallup Poll takes succeed forthcoming at smallest this seal to the faithfulness.
encircling 95% of all scantlings the Gallup Poll takes succeed forthcoming at smallest this seal to the faithfulness.
the sampling system is biased—otherwise the poll would frequently surrender the set-just rejoinder.
tclose are important nonsampling fallacys—otherwise the poll would frequently surrender the set-right
answer.

3. A Gallup poll reconnoitreed 3,112 significationrs. An AP poll reconnoitreed 778 significationrs from the corresponding population
on the direct corresponding investigation. How does the brink of fallacy for a 95% assurance intermission
compare for the Gallup and AP polls?
a. The Gallup brink of fallacy is bigger than the AP brink of fallacy.
b. The Gallup brink of fallacy is the corresponding as the AP brink of fallacy.
c. The Gallup brink of fallacy is smaller than the AP brink of fallacy.
4. The mediocre is 80 and the test rupture is 10. What is the test acenumerate for an observation
of 90? Profession your production underneath.
3

Suppose that the BAC of scholars who swallow five beers varies from scholar to scholar according to a
Normal classification forthcoming a while mediocre 0.07 and test rupture 0.01. For investigations 10 through 13, profession
your production underneath the investigation and transcribe your rejoinder in the verse.
5. The intermediate 99.7% of scholars who swallow five beers accept BAC natant what two entirety?

6. What percent of scholars who swallow five beers accept BAC underneath 0.09?

7. What BAC do the foremost 15% of scholars accept forthcoming swallowing five beers?

8. Sketch a Normal deflexion for the gist overhead forthcoming a while mediocre = 0.07 and test rupture = 0.01.
Label your x-axis from 0.04 to 0.10 in 0.01 increments. So profession the how the top 15% of
students (from #7) would be represented on that Normal deflexion.

9. A poker indicateer is dealt moneyless laborers for various hours. He decides to bet heavily on
the conclusive laborer of the slumbering on the postulates that forthcoming numerous bad laborers he is due for a
winner.
a)
b)
c)
d)

He’s just, owing the allurings accept to mediocre out.
He’s evil-doing, owing successive deals are dogged of each other.
He’s just, owing successive deals are dogged of each other.
He’s evil-doing, owing his expected allurings are $0 and he’s underneath that now.

10. The presumption of an outforthcoming of a purposeless wonder is
a)
b)
c)
d)

either 0 or 1, existing on whether the wonder can really take-place.
the rate of a very hanker order of repetitions on which the outforthcoming take-places.
the mediocre plus or minus two test ruptures.
the assurance equalize.

4

In empire postulates, a extraction consists of two or over living-souls who feed conjointly and are cognate by blood
or matrimony. Adopt an American extraction at purposeless and enumerate the reckon of fellow-creatures it contains. Close is
the assignment of probabilities for your consequence:
# of living-souls
Probability

2
0.42

3
0.23

4
0.21

5
0.09

6
0.03

7 or over
???

11. What is the presumption a extraction succeed accept 7 or over fellow-creatures in it? Profession your production underneath.

12. What is the presumption a extraction succeed accept over than 2 fellow-creatures in it? Profession your production underneath.

13. What is the presumption a extraction succeed accept 3 or 4 fellow-creatures in it? Profession your production underneath.

14. What is the expected esteem of the reckon of extraction members? Profession your production underneath and
transcribe your rejoinder in the unmitigated.
15. A accoutre of cards contains 52 cards, of which 4 are aces. You are offered the forthcoming place:
inhale one card at purposeless from the accoutre. You win $10 if the card inhalen is an ace. Otherwise
you risk $1. If you ascertain this place very numerous eras, what succeed be the mediocre consequence?
a)
b)
c)
d)
e)

encircling -$1, owing you succeed risk most of the era.
encircling $9, owing you succeed win $10 but risk simply $1.
encircling -$0.15, that is, on the mediocre you risk encircling 15 cents.
encircling $0.77, that is, on the mediocre you win encircling 77 cents.
encircling $0 owing the purposeless inhale surrenders you a just bet.

16. A accoutre of 52 cards contains 13 lifes. Close is another place: inhale one card at
purposeless from the accoutre. If the card inhalen is a life, you win $2. Otherwise, you risk $1.
Compare this place (circumvent it Place 2) forthcoming a while that of the anterior investigation (circumvent it Place 1).
Which one should you adopt?
a)
b)
c)
d)
e)

Wager 1, owing it has a surpassing expected esteem.
Wager 2, owing it has a surpassing expected esteem.
Wager 1, owing it has a surpassing presumption of alluring.
Wager 2, owing it has a surpassing presumption of alluring.
Both places are identical keep-apartial.

5

17. A psychologist apprehends that flattenening to Bach may aid fellow-creatures apprehend. She surrenders subjects a set of
puzzles and measures how numerous they clear-up in 5 minutes while flattenening to Bach. From postulates on
numerous fellow-creatures, the psychologist determines a presumption copy for solving 1, 2, 3,4 , and 5
puzzles clear-upd. The expected esteem she entirety from this presumption copy is 2.6. The law of
comprehensive entirety says
a) behold whether each of numerous subjects clear-ups a be-wilderment. The rate who clear-up a be-wilderment
succeed be seal to the expected esteem.
b) if you behold five subjects in a row who clear-up simply one be-wilderment, the proximate various subjects are
slight to clear-up three or foul-mouthed be-wilderments owing the mediocre must forthcoming seal to the expected
value.
c) the expected esteem is set-just simply in a purposelessized distributionately exemplification.
d) behold numerous subjects and chronicles how numerous be-wilderments each clear-ups. The mediocre succeed be seal
to the expected esteem.
The classification of tops of adult men is closely Normal forthcoming a while mediocre 69 inches and test
rupture 2.5 inches. Profession your production. Answers forthcoming a whileout set-just production succeed not admit any security.
18. What percent of all men are briefer than 64 inches?

19. How elevated is a man whose testized top is z = -0.3? Rejoinder in inches.

20. What percent of all men are elevateder than a man whose top is at the 60th percentile?

21. How elevated is a man who is in the 82nd percentile? Rejoinder in inches.

6

The casino frolic craps is fixed on flattening two dice. Close is the assignment of probabilities to the sum of
the entirety on the up faces when two dice are flattened:
Outcome
2
Probability 1/36

3
2/36

4
3/36

5
4/36

6
5/36

7
6/36

8
5/36

9
4/36

10
3/36

11
2/36

12
1/36

The most contemptible bet in craps is the “ignoring verse.” A ignoring verse bettor wins presently if either a 7 or an
11 forthcomings up on the pristine flatten. This is circumvented a “natural.” Use this counsel to rejoinder investigations 11
through 14.
22. What is the presumption of a probable?
a. 2/36

b. 6/36

c. 8/36

d. 12/36

e. 20/36

23. What is the presumption you do not flatten a 7?
a.

6/36

b. 28/36

c. 0

d. 30/36

e. 8/36

24. Gigi has flattened a probable on foul-mouthed unswerving tosses of the dice. This excites the gamblers standing
around the board. They should recognize that:
a.
b.
c.
d.
e.

Gigi has a hot laborer, so she is over relishly to flatten another probable.
The law of mediocres says that Gigi is now less relishly to flatten another probable.
Rolls are dogged, so the luck of flattening another probable has not modifiable.
Four unswerving probables are closely unusable, so the dice are probably loaded.
They should not be surprised owing the presumption of foul-mouthed unswerving probables is 2/36.

25. The board overhead professions a normal presumption copy owing:
a.
b.
c.
d.
e.

All the probabilities are natant 0 and 1.
All the probabilities are natant -1 and 1.
The sum of all the probabilities is directly 1.
Both A and C.
Both B and C.

7

26. A frolic involving a two of dice pays you $4 forthcoming a while presumption 16/36, costs you $2 forthcoming a while presumption
14/36, and costs you $6 forthcoming a while presumption 6/36. What is the expected esteem of the perfect of
specie you win or risk forthcoming one indicate of the frolic? Profession your production using 3 decimal places. An
rejoinder forthcoming a whileout set-just production succeed admit no security.

Fewer US teens steam, swallow than European peers: con-over
Fewer teenagers in the United States steam and swallow compared to their European enumerateerparts, but
over use garbages, according to a University of Michigan con-over released Friday.
Using postulates from 36 European enumerateries plus the United States, researchers plant that 27 percent of US
adolescents had consumed alcohol in the month precedent to gist quizzed by pollsters, compared to 57
percent of Europeans.
Twelve percent of American teens had steamd tobacco, compared to 20 percent for the Europeans,
according to the con-over, the fifth of its bark since 1995 forthcoming a while a sum of 100,000 scholars time-honored 15 and 16
taking keep-apart.
"One of the reasons that smoking and swallowing rates natant adolescents are so abundant inferior close than in
Europe is that twain behaviors accept been declining and accept reached historically low equalizes in the United
States," manage fabricator Lloyd Johnston said.
"But smooth in the precedent years of the European reconnoitres, swallowing and smoking by American adolescents
was perfectly low by similitude," he said, adding however that "use of unfair garbages is perfectly a opposed
matter."
Eighteen percent of the Americans had used marijuana or hashish, a rate exceeded in Europe simply
in France (24 percent) and Monaco (21 percent).
On mediocre, simply ssmooth percent of immature Europeans had used either gist.
Relatively not-difficult access to marijuana and unimportant awareness of its dangers teach the figures, according to
the responses that researchers placid from reconnoitre keep-aparticipants.
The Americans were so the biggest users of all other garbages as-well marijuana -- such as LSD, ecstasy
and amphetamines -- at 16 percent, compared to six percent over Europe.
"Clearly the United States has attained rateately low rates of use for cigarettes and alcohol, though not
as low as we would relish," Johnston said. "But the equalize of unfair garbage use by adolescents is quiet exceptional
here."
15,400 teenagers in the United States took keep-akeep-adeal-out in the reconnoitre, ahanker forthcoming a while at smallest 2,400 enumerateerparts in
each of the 36 European nations, the University of Michigan said in a propoundment.
8

27. What is the population of curiosity-behalf for this con-over?

28. Indicate the most relishly pattern of fallacy that could impression the ascertainings in this con-over. Teach your
choice.

29. What was the scantling extent for tribe from the US for the running year?

30. Reckon a 90% assurance intermission (CI) for the rate of U.S. teenagers that had used
marijuana or hashish (intermittently for the running year).

31. Suppose you were to substitute the assurance equalize in investigation 4 to 95% using the corresponding scantling.
How would the assurance intermission substitute? No calculations needful.
a.
b.
c.
d.

The assurance intermission would be the corresponding width but shifted to the left.
The assurance intermission would be the corresponding width but shifted to the just.
The assurance intermission would accept the corresponding core but would be travel.
The assurance intermission would accept the corresponding core but would be narrower.

32. What if the scantling extent was simply 5000 fellow-creatures for the 90% assurance intermission in #4. How would
the assurance intermission substitute forthcoming a while this smaller scantling extent? No calculations needful.
a.
b.
c.
d.

The assurance intermission would be the corresponding width but shifted to the left.
The assurance intermission would be the corresponding width but shifted to the just.
The assurance intermission would accept the corresponding core but would be travel.
The assurance intermission would accept the corresponding core but would be narrower.

33. A new-fangled poll reputed a assurance 95% assurance intermission of 52% ± 3%. The poll
was carried out by telephone, so fellow-creatures forthcoming a whileout phones are frequently embracing from the
sample. Any fallacys in the last results due to excepting fellow-creatures forthcoming a whileout phones:
a.
b.
c.
d.

are intervening in the propoundd brink of fallacy.
are in importation to the propoundd brink of fallacy.
can be ignored, owing these fellow-creatures are not keep-akeep-adeal-out of the population.
can be ignored owing this is a nonsampling fallacy.

9

34. The specialty “95% assurance” mediocres
a.
b.
c.
d.

our results are gentleman for 9% of the population of all adults.
95% of the population falls forthcoming a whilein the brink of fallacy we propound.
the presumption is 0.95 that a purposelessly chosen adult falls in the brink of fallacy we propound.
we got these results using a system that surrenders set-just rejoinders in 95% of all scantlings.

35. Gallup polled 1,523 adults and 501 teens on whether they generally common of constitutional gambling.
63% of adults and 52% of teens said yes. The brink of fallacy for a 95% assurance propoundment
encircling teens would be
a.
b.
c.
d.
e.

greater than for adults, owing the teen scantling is smaller.
less than for adults, owing the teen scantling is smaller.
less than for adults, owing tclose are fewer teens in the population.
the corresponding as for adults, owing they twain forthcoming from the corresponding scantling reconnoitre.
Can’t say, owing it exists on what percent of each population was in the scantling.

36. Which of the forthcoming systems would lessen the width of a assurance
intermission for a mediocre, if all else forthcomings the corresponding. You may adopt over than one rejoinder for
this investigation.

a.
b.
c.
d.

Increase the equalize of assurance.
Increase the scantling extent.
Decrease the equalize of assurance.
Decrease the scantling extent.

37. A 95% assurance intermission indicates that:
a. 95% of the likely scantling mediocres (same-extent scantlings) succeed be intervening by the intermission.
b. 95% of the intermissions fabricated using this regularity fixed on corresponding-sized scantlings from this
population succeed comprise the scantling mediocre.
c. 95% of the likely population mediocres succeed be intervening by the intermission.
d. 95% of the intermissions fabricated using this regularity fixed on corresponding-sized scantlings from this
population succeed comprise the population mediocre.
38. A nationally exclusive garden counselpaper conducts a reconnoitre natant scholars nationwide every
year. This year, responses from a pure purposeless scantling of 204 garden scholars to the investigation
“About how numerous CDs do you own?” resulted in a scantling mediocre of 72.8. Fixed on postulates from
anterior years, the editors of the counselpaper succeed affect a population test rupture of 7.2.
What is a 95% assurance intermission for the population mediocre reckon of CDs owned by all garden
students? Profession your production.
a.

(65.6, 80.0)

b. (71.8, 73.8)

c. (72.0, 73.6)
10

d. (72.3, 73.3)

39. The perfect sharp-end of doing a assurance intermission is:
a. To get counsel encircling the scantling statistic.
b. To do a census.
c. To think the test rupture.
d. To think the population parameter.

11

Practice Exam Answers
1. D
2. C
3. C
4. 1
5. 0.04 and 0.10
6. 97.73%
7. 0.081
8. Profession a Normal deflexion forthcoming a while 0.07 in the intermediate and 0.04 to 0.10 conspicuous in smooth increments at
proper spacing on either verge. A verse should be inhalen at 0.081, forthcoming a while shading to the just of that
verse and the shading labeled forthcoming a while “top 15%.”
9. B
10. B
11. 0.02
12. 0.58
13. 0.44
14. 3.14
15. C
16. A
17. D
18. 2.5% (or 2.27% using the board)
19. 68.25
20. 40
21. 71.25
22. C
23. D
12

24. C
25. D
26. 0
27. All US and European teens
28. Response fallacy b/c fellow-creatures capability lie (other rejoinders are right, but succeed exist on the
rationale)
29. 15,400
30. Scantling rate is 18% forthcoming a while n = 15,400. The assurance intermission is (0.1749, 0.1851) using Z* =
1.645, but either 1.64 or 1.65 could be used.
31. C
32. C
33. B
34. D
35. A
36. B, C
37. D
38. B
39. D