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Unformatted text preview: Instructor Class Meeting Time Red Id STAT 119 EXAM ONE
February 28, 2007
Form A You have 90 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 after 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 CAPITAL LETTERS in the space provided for the
multiple choice. BE CAREFUL! GOOD LUCK! Page 1 Total
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Page 8 Total Total A 1 Multi ie choice uestions are worth 2 oints each 1. Which is true about bar charts?
A. A bar chart is for quantitative data.
3. A bar chart has bars that touch.
© A bar chart has categories on the xvaxis
D. Both ’0 and c are correct. Answer: 2. A researcher collected data from 1000 undergraduate students on how many hours they spend
studying per week for their classes. The majority of the students study around 8 hours per week,
whereas only a few students study more than 18 hours per week. Which of the following
statements is true: A. The mean for this distribution is larger than the median since the distribution is
’ negatively skewed.
@The mean for this distribution is target than the median since the distribution is positively
skewed, C. The mean for this distribution is smaller than the median since the distribution is negatively skewed. D. The mean for this distribution is smailer than the median since the distribution is positively skewed. Answer: 3. Suppose we want to learn something about Major League batting averages over the past ﬁve
seasons. If 100 of the players who piayed in all of the past five seasons are chosen and their
collective batting average was 0.274, what is true about that vaiue? A. 0.274 is the batting average of the population in question.
B. The value does not give us any real information. C. This is the data that we gathered @ This is one of our summary statistics from the sample. Answer: 4. The grade distribution for a Spanish exam was normed, with a mean of 72 and a standard
deviation of 8. The distribution for a Statistics exam was also normain distributed, but with a
mean of ’74 and a standard deviation of 6. A particuiar SDSU student got a 68 on the Spanish
exam and a 70 on the Statistics exam. On which exam did the student do better, relative to the rest oftheclass? 2:” m ~, j: _..  “A “A; it
A); Statistics wtﬁmiﬁ é g F???” {agitating €in 3: Spanish I” C. They did equally weil on both exams L: w— ig} .. ﬂ _
D. There is not sufﬁcient information provided to answer the question. a: M“ if} s is?” 1}
Answer. Total: (8} 5. A Zuscore of 2 means
A. The observation is 2 standard deviations smaller than the mean The observation is 2 standard deviations larger than the mean
C. The observation is twice larger than the mean
D. The difference between the observation value and the mean is 2 Answer: Below is information about student success in Stat 1E9 last semester. Use information from the table
to answer uestions 67. ——
605 224
583 281 6. Among all students in stat E19 last semester, what proportion were femaie students who passed
the course? A. 0.4907 B. 05103 C. 0.6748 @0.3444 Answer: 2:. 7. Among males, What proportion failed Stat 119 last semester? A. 0.4436 @2702 C. 0.7298 D. 0.1323 Answer: M/ f: if} a2... a 8. All of the foiiowing are characteristics of the correlation coefﬁcient except;
A. The correlation coefﬁcient is unitless
B. The correlation coefﬁcient can indicate the direction of an association.
C. Data used to calculate the correlation coefﬁcient must be quantitative. The correlation coefﬁcient cannot be negative.
E. The correlation coefﬁcient can indicate the strength of an association. Answer: 9. Temperature Distribution for the month of July in San Diego is normal with a mean of 71 degrees
and standard deviation of 3.3 degrees. 84 percent of July temperatures fall under which value? A. 67.7 B. 77.6 c. 80.9 r). 64.4 74.3
Answer: “ W" ' i
E J "E Total: (10) .J g }
/..........m. i 47:: 3% titan A 3 Use the following for problems 10—11: It is difﬁcuit to accurately determine a person’s body fat withOut immersing him or her in water. Hoping
to find easier ways to estimate a person’s body fat, researchers immersed 20 male subjects and recorded
their body fat percent, measured their waist and recorded their weights. It was found that Predicted % of body fat = 27.4 + 0.25 (weight) and R2 = 48.5% it was also determined that Predicted % of body fat = 432.6 + 2.22 (waist) with the variability in percent
of body fat due to waist size equal to 78.7%. 10. Which measure is a better predictor of the percent of body fat? Waist
B. Weight
C. They are equaiiy good predictors
I). Can’t be determined from this data Answer: 11. interpret the siope of the regression equation relating percent body fat and weight
A. F or every 1 unit increase in percent of body fat, weight increases by ~27.4 lbs.
8. For every 0.25 unit increase in weight, percent of body fat increases by 1 unit.
@ For every l unit increase in weight, percent of body fat increases by 0.25 units.
D. A person with 0% body fat will have a weight of 27.4 units. W 12. A large high school has 600 senior students, all of whom are enrolled in a ﬁrst period homeroom.
There are 24 senior homerooms, each with 25 students. A school administrator decides to select a
sample of 75 seniors. He selects three of the senior homerooms at random, including ail of the
students in the selected homerooms in the sample. What type of sampling is this? A. Simple Random Sample B. Stratiﬁed Random Sample Cluster Sample 3). Systematic Random Sample. Answer: f“?
V 13. in order to investigate whether women are more likely than men to prefer Democratic candidates,
a pohtical scientist selects a iarge sample of registered voters, both men and women. She asks
every voter whether they voted for the Republican or the Democratic candidate in the last
election. This is {E} an observational study
B. a matched~pairs experiment
C. a completely randomized experiment
I). a block design. Answer: Total: (8) 14. Suppose the IQR of the SAT test was caieulated to be 200 points. 75% of the students scored
more than 500. Which of the following statements is correct:
A. 50% of the SAT scores lie between 300 and 500. reg The median of the SAT scores is 600. @i 1:: ‘3 ’“ {:3
g} 50% of the SAT scores lie between 500 and 700. 43 m “I r W
D. Both A. and B. are true. {t Wﬂgwgk} E. Both B. and C. are true. 15. One hundred volunteers who suffer from severe depression are availabie for a study. The
volunteers are ﬁrst divided by gender. Half of the men, and half of the women, are seiected at
random and are given a new drug which is thought to be particularly effective in treating
depression. The remaining men & women are given an existing drug for treating severe
depression. A psychiatrist evaluates the symptoms of ali volunteers after four weeks in order to
determine if there has been substantial improvement in the severity of depression This would be
an example of A. replication
B. confounding a block design . a matchedpairs design. Answer: Use the following 333911 for Igrobiem 16_ mermaidi5 “winter's” 90 95 '. mo :05 no; [gm .._ :_ .. 16. The NBA conducted a study to analyze the correlation between the average number of points
scored per game and the number of wins for each NBA team. Which of the following correlation
coefﬁcients would most accurately describe the ab0ve relationship? Weak, Positive Correlation
B. Weak, Negative Correiation
C. Strong, Positive Correlation
D. Correlation cannot be distinguished from scatterplots. Answer: g
Total: (6) A 5 Use the fotlowing information to answer Emblems 1720 [i7 goints): How much sodium is in breakfast cereal? The stem and leaf plot below lists the sodium content in a single
serving for a sample o®opular cereals.
The leaf unit for the sternplot is tens (so 0 i 7 = 70) NNMMQQ caesium
\Dwqh 17. (4 points) Find (and clearly label) the ﬁve number summary for this data. file‘s ‘% §%&‘§§€% _ 3g Stiles
a Wis .223; 22% is 18. (4 points) Frosted Mini Wheats has 0 mg of sodium per serving. Is this value an outlier? Show all
work for credit. Esseszeﬁwtos": 323 k
inisgﬁfﬁﬁ w getgwiggiféﬂ :sit‘ts
@iwgﬁﬁtg xiteg wﬁidﬂ'} $W<%. 7e35,; {Stefﬁ is {a mi 32:3 {xiiitag“ 19. (5 points) Constru a modified box piot for the sodium content data. You must Eabel clearly to
receive full credit {3* i 53% i? 3 I? ii ass sw—WWWM' é .
WW} 3.43; G
0 50 100 1 50 250 300 20. (4 points) Calculate the IQR and standard deviation for the data above. Which is the appropriate
choice of spread for the data set? Justify your choice. IQR: Standard deviation: “if i ‘* 1&3 ChOice of spread: E 51*; Kilmaii wish {a {as as s. a aims; is: etQieiss titer; samea Total: (17) k2 Justiﬁcation of choice: ' IX “3 EN add; $3}
21. (5 points) The time it takes to play a college baseball game varies according to a normal
distn'bution with a standard deviation of 20 minutes. If only 2% of the games last less than 100
minutes, what is the mean length (a) of these games? «egg: Wang
W. WM, 1:: {a $53 , f
» News ~ i ‘s"‘°i’;}‘{et\) fit: Egg“; «f gtbbn. as} ‘
Answer: ’ 33%;: “at; i Lei i’iat‘zfeetiiis
Use the following to answer groblems 22~23 (6 points):
The length of human pregnancies from conception to birth varies acoording to a normal distribution with mean 266 days and standard deviation 16 days. Use the Empirical Rule to answer the foltowing:
22. (3 points) What proportion of pregnancies last between 250 and 298 days? H.1 Answer: Use the following information to answer Emblems 2425 15 {pints}: A survey was conducted in a Caiifornia High School District. A random sample of ﬁve empioyees was
selected from each of the ten schoois in this district, and their salaries were recorded. The histogram
belowshows the salaries of the SO empioyees, in thousands of dollars, for this year. . .535“, ft“: €33 _ W ﬁx q i no
s’tfxggﬁrt Cm : R 3 J“ ‘3
{gist tie: it see W % 5; EE
‘3 a
24. (2 point) What sampling method was used? gi‘i’gﬁi 25. (3 points) What salary interval contains the ﬁrst quartile?
W W “*3
,a s 5 Am 3, ﬂ Total: {16)
€2$$ “‘"’ Esta i {39" r A {fee the following information to answer amblems 2&28 i9 {ﬂimsy A consumer group decides to test the eﬁeettveness of a new “organic” launéry detergent. They
intentionally get grass stains on a sample of 60 white T—shirts in order to see how well the detergent will
clean them. Each shirt is randomty assigned to one of three water temperatures (cold, warm or hot); and
one of two wash cycles (regular or delicate). The level of cleaning for each shirt is recorded on a scale
from one to ten; the person evaluating the cleaning ievei is unaware of the treatment used on the shirt. The
average clean ing level for each treatment group is calculated. 26, (5 points) identify the following for the experiment: I. Explanatory variable(s}
'3. Response variable . " f,
x": _ .3 ﬂ i f ,
111. Number of treatments f> >5 2:; w 9‘ y: ﬁg‘ﬁg
W. The expenmental units are: mg » 3:; lg é?” "SEE
V. What type ofvat‘iable is “water temperature”? 27. (2 points) Circle the correct anewer:
The average cleaning level is a: Parameter
28. {2 points) Is blinding useé it} this experiment? Efﬁe Explaie (in oee sentence) the reason for using blindng in an experime t. . a,
h t t n» eewealﬁﬂt {E 9&1?" gamete Wei 5:; 2, Liérei ee’eﬁa 9&1} are :3 {:5} 3 {ﬁg £33 if i .. = g are e” lxeieﬁ We‘lﬁmeéée ea {lg 3i” “‘3 WE’LL“: l l l Use the follewing to answer emblems 2930 £18 gointsz: The number of penalty yards per game for NFL teams is normally distributed with a mean of 35
yards/game and a standard deviation of 6 yards/game.
29. (5 points) What proportien ofNFL teams will have peealties of between 30 and 45 yards per game? « . \
@334; xee’i} AM.»
gfieew’ee a; %¢%3'“3"3\
we; MM. it;
Answer: a» W» m k ~ {m t We;
'31 eﬁeeg Meaee’é ‘2 ~ {wen we
3%. {5 points) Betweee what two values are the central 60% ofthe teams’ penalty yards per game?
fige $1.; {e} e e3; z; gee:
' I i f» ﬂ 5 9 r" W s I“; ‘ {:3 U {Bageli ‘7 [ﬁx M ix
Riva :: e2 we we M ee l? g: *3, Answer: A 8 Use the following information to answer problems 3135 116 points): A start~up company has developed an improved electronic chip for use in iaboratory equipment. The
company needs to project the manufacturing cost, so it develops a spreadsheet model that takes several
business costs into account. The spreadsheet estimates the cost of producing 10 thousand to 200 thousand
chips per year. The number of chips produced (10003) and cost per chip ($) are recorded. The following
regression equation was obtained:
Cost 3 101 « 0.431 Chips
The percent of variability in cost per chip that is explained by the regression of cost on number of chips
produced is 67.7%
31. (4 points) Find the correlation coefﬁcient and use it to interpret the reiationship between these
two variables, W Correlation coefﬁcient: ‘ " Interpretation 4 . 3, 2 f. g {a ._ . =; of“ .56? g
enema a {Inactive Mean" fetai‘i‘tftté‘?” a “t: “3 is“ iii W awe”? J
a} (S General: A ,w . . i
agree gatest timid anti pet“ a.in ' ' r m. . .  a , ‘r i \ a" t” rear“ as if" r“ 53 Spec‘ﬁCgflm {Léﬁéog 951:}. we {{{gajgigé {Cei‘ tintiamﬁf 32. (5 points) Suppose it is known that a production level of 160 thousand chips results in a cost per chip of $37.47. Calculate the residual for this modei value.
f1 Qwiaiw adamant)" :§”s’twoi.§§ The followingmigsidual piot wwamswobtained for the model described above: Wmepmz i
i
l E"
E
z
s
 33. (3 points) Will the model overestimate or underestimate the cost per chip for a production level of
100,000 chips? Use the residual plot to justify your answer. tesiomai its: negating {on C} <7» <4”: 3 h p E
En uterine teen. a: is its; i/Ltiﬁig {negates titeaaiieiw 34. (2 points) Use the residual plot to explain whether a linear model is appropiiate for this data set:
Queueiiteea, a: pa use: if“ a. die tenet/tad a W“ 3 as tea.an saga £3; at; r nonsense: eait’w“
35. (2 points) What range of values for costs would it be reasonable to predict using this model? ﬁr g 4 M was; 551%.; ‘ {Epigé’i
Kai‘s 3:; e iii ii {iii ii“ I g “"5 1:}Totai: (16)
$1 w § M EL #2; 3 j J: Ea; K a ﬁg; (7; a to; city’s: i. Steed Ewing stars a, ineng ...
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