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Unformatted text preview: Section 24 Name Red Id STAT 119 EXAM ONE
February 28, 2008
Form D You have 75 minutes to complete this exam. Mark your answers neatly on the exam and be sure
to Show all your work. Please round your answers to four digits afier the decimal when possible.
Make sure to put your final answers neatly Within the answer boxes (when provided). Please
CIRCLE the correct answer and use CAPETAL LETTERS in the space provided for the
multiple choice. BE CAREFUL! GOOD LUCK! Page 1 Total
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Z=X"”
cs D Multigle choice Questions are worth 3 QOilltS each 1. Jack scored 82 on a test in which mean was 76 with standard deviation of 7. Jill scored 85 on the
test in which mean was ’78 with standard deviation of 8. if the scores are normaily distributed,
who scored better on their test i'eiative to the rest of their class? A. Cannot be determined, because they are in different classes
B. Jack, since his z—seore was higher
@ Jili, since her z—score was higher
D. Jack, since the standard deviation was smaller
E. Iiii, since the mean was higher Answer:  2. in generai. which of the following statements is FALSE?
A. if a distribution is symmetric, then the mean wili be equal to the median.
B. The sample mean is more sensitive to extreme values than the median.
© The iQR is more sensitive to extreme values than the standard deviation.
D. The sample standard deviation is a measure of spread around the sampie mean. f” 3. Beiow yon wiil ﬁnd a histogram of the average wind speed in miles/hour of 43 days in Hawaii. a D  Frequency 1) SF) 9:: we 4!) hr) air) (“1) Wind speed Which of the foliowing statements regarding the distribution above is INCORRECT? A. Because of the gap in the distribution, the one day in the (06) mph intervai is iikely to he an
outiier. Bil The median wind speed is in the (45—50) mph interval and the third quartile is within the (50
55) mph interval. C. The median wind speed is in the (4560) mph interval and the ﬁrst quartiie is within the (35—
40) mph interval. 1). The distribution of wind speeds has a negative skew. Answer:
Teta}: (9) 4. A market researcher randon’dy selected two italian restaurants from ail Itaiian restanrants in Old
Town and interviewed ali customers in each restaurant. What sampling method was used?
@ Cluster Sample
B. Convenience Sample
C. Simple Random. Sample
D. Stratified Sample Answer: 5. What couid go wrong with the particniar sample selected in the previous problem?
A. The restaurants are selected at random; the data is therefore .relativeiy unreliable.
B. The sample size may be too large, which makes reading the data difﬁcult. C. The customers selected from a restaurant may create an unbiased sample.
@ The chosen restaurants may not accurately represent ail Itaiian restaurants in Oid Town. Answer: 6. On a given day, the NYSE opening price per share for the 100 largest US. corporations has a mean of $385 and a median of $92. We can conclude:
The distribution of the price per share is symmetric. The distribution of the price per share is skewed to the right.
_ The distributiOn of the price per share is skewed to the left.
D. " There mast be a mistake: there is too large of a discrepancy between the mean and median. Answer: 7. An IQ test follows a normal distribution with a mean of 100 and standard deviation of 21.
84 percent of IQ scores will faii above which value? @79 Answer: 8. John is enrolled in a calculus course and has received his score on the midterm exam. His score
on the midterm was 114, and the professor has indicated that his zscore was 0.78. What is the best interpretation of the meaning of this z~score7 B. 142 C. 58 D. 84 E. £21 A. Seventy—eight percent of all students taking the exam had scores below his.
17 Seventymeight percent of all students taking the exam had scores above his. His score was 0.78 standard deviations above the mean of all scores.
D. His score was 0.78 IQR above the median of ali scores.
E. He got 378% of the problems on the test correct. Answer: Totai: (15) I‘d 9. The histogram beiow was generated by 21 Stat E19 cEass. It shows the heights of a sample of
freshman students. ﬁl‘ﬂiiﬁﬂwﬁ it was determined that the outlier on the left resulted from a height being incorrectiy entered. This
incorrect data point was removed from the data and a new histogram was made and all new
statistics were calculated. Which of the foiiowing statements is/are true? When the incorrect data
point is removed: A. The mean and standard deviation wiEl both be larger B. The mean and standard deviation wiii both be smaller The mean will be larger, but the standard deviation will be smailer
i). The mean wiil be smaller, but the standard deviation wiEl be Earger
i3. None of the above . f;
Answer. it}. A State University group is interested in'whether voters would support lowering the iegal drinking age to £8. They have chapters on each of California’s major universities. Each of these
chapters randomiy selected 25 students and asked whether they approve of lowering the drinking
age. The most signiﬁcant bias introduced here is: A? Undercoverage . Convenience Sampling
C. Response Bias
D. Noe Response Bias Answer: 1 i. in the context of regression analysis. which of the following statements are always true?
I. Outiiers will affect the value of coefficient of determination. w?
H. When the sum of the residuals is greater than zero, the model is nonlinear. g
Ill. A point has high ieverage if including it results in a different regression model}? . E only ll only 111 only . I and ii oniy i, it, and III Answer: Total: (9} meon> 1.2. A researcher uses a regression equation to predict home heating biils (doilar cost), based on home
size (square feet). The correiation between predicted bilEs and home size is 0.70. What is the
correct interpretation of this finding? A. For each added square foot of home size, heating bilEs increased by 49 cents.
B. 70% of the variabiEity in home heating bilis can be expiained by home size.
if? 49% of the variabiiity in home heating bills can be expiained by home size.
. For each added square foot of home size, heating biiis increased by 70 cents.
E. None of the above. Answer: at"? 13. Which of the foilowing is always false regarding residaai plots?
A. A large residual indicates an overprediction.
B. A negative residuai indicates an overprediction.
C. A small residual indicates a good prediction at that particuiar data point.
D. Patterns in a residual plot as a whole indicate poor predictive power.
Q Uneven variation in a residue} plot indicates strong predictive power. Answer:
see l4. The boxplots below summarize the distributions of SAT verbal and math scores among students
at an upstate New York high school: WW 5
a
i
 Math
s
E
e Verbal Boxglnt of Math, Verbai . l p . '
389 466 500 500 7'00 865 Which of the following statements is false?
A. The range of the math scores equals the range of the verbal scores.
{7?th The verbal scores are roughiy symmetric, while the math scores are skewed to the right.
. The highest math score equals the median verbal score.
D. The interquartiie range for the math scores is smaller than the interquartile range for the
verbal scores. Answer: Totai: .(9) D Use the followin information to answer roblems 1519 .
Hurricanes deveiop low pressure at their centers. A sampie of 163 hurricanes (with centrai pressure
ranging from 910 to 1000 'rnb) was studied to investigate the relationship between central pressure (rob)
and maximum wind speed (itnots). The data was analyzed to produce the results below: Regression equation: Max wind Speed 2 955.27 — 0.917Central Pressure Rsquared m 79.21% 15. (6 points) What is the correlation between the central pressure and maximum wind speed? Use
this vaiue to assess the strength of the linear association. W s... gee? ﬁw
Correlation coefficient: fewer“ ii i g lg” Interpretation 3 ﬁggéigrg Egg” illicit: W it i.
tesheé ' series. 5 {satires toting Slope: Interpretation $3.;
gfﬁﬁieﬁ a; {neat l7. (6 points) Hurricane Katrina had a central pressure of 920 rnb. If the residual for this model value
is ~i3. what is the true maximum wind speed for this central pressure? gﬁdsﬁ term care {aisle iii“ 53 gesideei ﬁstmi;
sang/Es : m ililéé st; ‘11: trig tageta e%%.§g
Answer; é i8. (3 points) A hurricane has a calculated residual that is negative. Which of the following is a
correct statement? The residual vaiue indicates that the prediction is too high
. We cannot determine whether the prediction is too low or too high from a residuai value.
C. Since the residual is negative the prediction must be accurate.
D. The residual value indicates that the prediction is too low. Answer: 19. {4 points) Would it be appropriate to use the above model to predict maximum wind speed for a
hurricane with centrai pressare l. 100mb? Expiairt why or why not in a full sentence. ~ K’s Total: 125} 20. (4 points) The mean value of land and buildings per acre from a sample of farms is normaily
distributed with a mean vaiue of $1508 and a standard deviation of $200. Use the Empirical rule
to estimate the percent of farms whose land and building values per acre are between $900 and $1700.
3:; if :1” tease“
& $5., Use the following information to answer problems 2123 520 Quintsg: A physicalﬁtness association is inciuding the mile run in its secondaryschool fitness test for students.
The time for this event is normality distributed with a mean of 440 seconds and a standard deviation of £32
seconds. 2.1. ('7 points) What proportion of secondary—school students have a mile run time t ‘ t is slower than 9 minutes (540 seconds)? gig e? EE%§} if ?£%§ : {:3 W éwiéﬁ E
its 2 I;
:: fie n siege} :2 Ewe ﬁgﬁifg ADSW’BI': g ﬂ .7 I" AriWWW” m  g 22‘ {7 points) What proportion of secondary—school students have a mile run time between 410 and 500 seconds? ééfég ﬂag {1 Answer: it 5;: 23. (6 points) If the association wants to designate the fastest 8.5% of secondary schoot students as
“excelient”, what time should the association set for this criterion? its is :asst’eeesse w n ESL éég Answer: E i Total: (26) 24. (7 points) The board of examiners that administers the read estate ‘orokers’ examination in a
certain state found that the scores were normally distributed with a standard deviation of 63. If the passing score is 480, and oaiy the top 34% pass the examination, what is the mean score on the
reai estate brokers’ examination? hgﬁﬂieigéggttgﬁ
3Q %ﬁ%eewiasis;i
‘5 :2? Use the foilowing to answer probiems 2528 £23 points}: The houriy earnings (in doilars) of a sample of 15 restaurant workeis are shown below:
9.1 10.7 11.1 13.5 it] 11.8 E22 12.4 12.5 12.6 12.8 12.9 13.1 13.2 13.4 25. (6 points) Construct a spiibstem piot for the data 5
§ g
Q a... as gee save 27. {6 points) Is the hoariy wage of $9.1 an outiier? Ciearly show ail work.
Ease: Ease: was as» We? Egg 53$; £5;
:___: beige 3;. gigs... gﬁiiiw‘i :%ti§. i §
52, eeiia.
i a a» 3 see a; sea a aiisah 2:» ¥¥~s3 .3 gﬁﬁg 28. (6 points) Caicafate the standard deviation and IQR for the distribution. Which is the best choice
of spread for this distribution? Justify your choice in one sentence: Standard deviation is; ‘3 a; g IQR i a g Choice of Spread 3 Q £12» Justiﬁcation of choice Ag ’ . Totai: J39) D Use the foliowing to answer problems 2932 519 points!: A random sample of £027 adults was classiﬁed by party affiiiation and whether they would support a
mandatory Heatth care pien. } Support Oppose i Unsure i Total E Democrat 261 l 156 15 l 432 l
i Repnblicatn 205 l 241 I 4 l 450 l
 Independent  82 l 45  18 145 I
 Total l 548 I 44:; l 37 i 1027 l 29. (4 points) What percent of alt adults were Republican and oppose a mandatory health plan? 30. (4 points} Of the Independent voters, what proportion support the mandatory heeith pien? 36% ﬁe tgégg
Age Answer g §§W 31. (6 points) ) Complete the tabie below to Show the conditional distribution of mandatory health
plan opinion. conditioned on party affiiiation. Show your work for fuil credit. Democrat W m i
3 E
i Repuhiican g??? ’1: m i
i
i W ﬁe g?
Independent in ﬁg: :2; tee tee? 32. (5 points) Do you think that party affiliation is independent of suppoﬂ' of a mandatory health care plan? Explain. g g I §
eiee ig genie zeéneeee tee engine nee new ﬁne
i S ’1‘ * 3 t? = ‘ Sweet“ r tine? nee Totalzwﬂ9) ...
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