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Unformatted text preview: /}P_—_'——#—__—————_———_——_—— Name I» ' _ _
Instructor Section number LEI STAT 119 EXAM ONE
October 15, 2003
Form A You have 2 hours to complete this exam. Mark your answers neatly on the exam and
be sure to show all your work. Please round your aswers to the nearest hundredth
(two digits after the decimal). BE CAREFUL! GOOD LUCK!‘ Page7 #21 \ ‘ #22 Pages #23 Page9 #24 Page 10 #25 I 2.
Total I b 7/ Multiple choice (4 points each) 1. All of the following are examples of categorical data, exgpt:
a) favorite color. ‘ W
c Tax bracket
(1) Final letter grade in a course (A, B, C, D, F) 2. Which of the following properties of the Normal distribution is NOT
true? a) It is symmetric about its mean
b)_ Its mean and median are equal c It is bell shaped .  It is uniquely deﬁned by two parameters, the mean (a) and
r standard deviation (0) .
e) None of the above are false 3. The histogram below gives the distribution of heights of 64 students in a statistics course.
20 '59 62 65 68 71 74 77 30
Height of the following is a correct statement?
’ 3.) Approximately half the students have heights between 65 and 71 inches.
1)) The histogram is symmetric.
A The tallest person must have a height of at least 79 inches.
6’ Approximately 28% of the students have heights between 62 and 65 inches. Q—i—
%0"wo Multiple Choice Answers oi 2i 3_lD_ .J 4. Consider the following scatterplot of two variables X and Y. 2.0 u
1.8 . ' ‘ .
I I
1.6 n I
I I
in." 1.4 I I I I
1.2 I a
1.0 I 
l————+——+—————l——t
1' o 1 5 2.0 2.5 3 o
X
We may conclude
a) The correlation between X and Y is close to 1 because there is a nearly perfect 
relation between them.
b) The correlation between X and Y is close to 1 because there is a nearly perfect
relation between them. c) The correlation between X and Y is close to 0. d) The correlation between X and Y is 0.50.
e one o e aove 5. Which of the following pairs of events are disjoint?
a) A: the odd numbers; B: the number 5
' b) A: the even numbers; B: the numbers greater than 10
c) A: the numbers less than 5; B: all negative numbers
d) A: the numbers above 100; B: the numbers less than —200 e) A: negative numbers; B: odd numbers 6. A researcher conducts a study on 120 subjects, all over the age of 50, to investigate the
effect of exercise and diet on mood. The factor(s) in this study are a) Mood b) Age c) The number of subjects (1) Exercise and diet 7. To avoid working late, a quality control analyst simply inspects the ﬁrst 100 items
ﬂ' day. This example is E) sampling.
a) onvenien b) Voluntary c) Unbiased ‘ 6 Random 6) Stratiﬁed Multiple Choice Answers ‘LL LL 6_Ci_ 7....Q... 8. If two events are independent of each other then which one of the following statements
is NOT correct? f a P(A and B) = P(A)* P(B) a) The outcome of the ﬁrst event cannot inﬂuence the outcome of the second. a) P(B l A) = P(B)
. P(A or B)= P(A) + P(B) 9. Which of the following statements is NOT true? \“aLIn a symmetric distribution, the mean and median are equal
\bldThe ﬁrst quartile is another name for the 25th percentile
. ‘ e median lies between the ﬁrst and third quartiles
@‘ e median is always greater than the mean
 The range can be obtained by subtracting the smallest value from
the largest value in a sample 10. The owner of a chain of supermarkets notices that there is a positive correlation
between the sales of beer and the sales of ice cream over the course of the previous year.
Seasons when sales of beer were above average, sales of ice cream also tended to be
above average. Likewise, during seasons when sales of beer were below average, sales
of ice cream also tended to be below average. Which of the following would be a valid
conclusion from these facts? a) Sales records must be in error. There should be no association between beer and
ice cream sales. b) Evidently, for a signiﬁcant proportion of customers of these supermarkets,
drinking beer causes a desire for ice cream or eating ice cream causes a thirst for
beer. 0) A scatterplot of monthly ice cream sales versus monthly beer sales would show
that a straight line describes the pattern in the plot, but it would have to be a
horizontal line. The observed correlation is most likely the effect of a lurking variable, such as
time of year. c) None of the above. 11. In a study of trees it was found that greater amounts of rain in a given year produced
tree rings of greater width. The correlation coefﬁcient for the two variables (rain fall and
tree ring width) was found to be ' b) negative Q—equelteneno.
Warm—L _ Multiple Choice Answers 9L 10_D__ 11_B__ 12. A public opinion poll wants to determine if Americans approve of drilling for oil in
the Artie Wildlife refuge. They select a simple random sample of 100 voters in each
state, bring these together for an entire sample, and ask if they approve of the drilling.
This is an example of a) A s stematic county sample.
c) A convemence sample.
(I) A simple random sample. 13. A study examined the relationship between the sepal length and sepal width for two
varieties of an exotic tropical plant. Varieties A and B are represented by x's and 0‘s,
respectively, in the follpwing plot: is no.
1 1.2 '0...
C
n 0.9 .a
In.
‘10.4 ""3
h I—l——l—l—
o 3 s 9 12
width Which of the following statements is FALSE? a) Considering variety A alone, there is a negative correlation between sepal length and
sepal width. b) Considering variety B alone, the least squares regression line for predicting sepal length from sepal width has a neativ . O   Wm.. . a  g n “varieties'togetheﬁthﬁeis‘a'pBWVE’E'Gﬁ‘eTa'ﬁon  e
ength and sepal width.
d) Consr   = ' length and sepal width. 14. A stack of four cards contains two red cards and two black cards. I select two cards,
one at a time, and do not replace the ﬁrst card selected before selecting the second card.
Consider the events A = the ﬁrst card selected is red, B = the second card selected is red.
The events A and B are a) Independent events. b) Disjoint events. c) Conditional events. (1) None of the above. Multiple Choice Answers _12_I§_ 13 ﬂ, 1440.— 15. A study of human development showed two types of movies to groups of children.
Investigators compared the number of crackers eaten by children watching the different
kinds of movies. One kind of movie was shown at 8 AM (right after the children had
breakfast) and another at 11 AM (right before the children had lunch). It was found that
during the movie shown at 11 AM, more crackers were eaten than during the movie
shown at 8 AM. The investigators concluded that the different types of movies had an
effect on appetite.
The response variable in this experiment is: w ‘ ' "’ n e different types 0 movies. 0) The time the movie was shown.
(1) The number of children. 16. At a small Midwestern college, 60% of the students are female , so P(F)=0.6, 70% of
the female students are liberal arts majors, so P(LA/F)=.0.7, and 50% of the male students are liberal arts majors, so P(LA/M)=0.5. A student is selected at random to represent the
school at a conference. The probability that the selected student is a male liberal arts major, PgM and LA) '5:
.4 3 a) 0.30 ) ‘ (.5 b) 0.40
c 0.50 m9
17.A town’s January temperatures average 36° F with a standard deviation of 10° F,
while in July the mean temperature is 74" F with a standard deviation of 8° F. In )0} I which month is it more unusual to have a day with a temperature of 55° F? 2 Janet d) They are equally unusual 5957(0671
c) There is not enough information to answer this question. 18. Pulse rates are useful in monitoring medical conditions. For 52 adults, the summary statistics of their pulse rates are given below: W
Min=50 Ql=68 Med=73 Q3=78 Max=96 . . . . . “2 0 70 ‘30 ‘lo me
Which of the followmg pulse rates would be consrdered an outlier by the cntenon? a) 55 b) 89 c) 90 d) 51 e) 92 Multiple Choice Answers ‘15 A 16 Ed. 17 B 18 g Short Answer Questions (34 points}: 19. (8 points) To test the hypothesis that shelf placement inﬂuences sales, a marketing
researcher has collected data on sales in a random sample of 15 comparable
supermarkets. Each supermarket was randomly assigned one of 3 different shelving
policies for an identical brand of soup. The data is weekly sales ﬁgures of cans. bottom shelf middle shelf top shelf sales sales sales
100 250 100
50 200 100
100 250 200
100 300 200
150 500 400 a) (2 points) What are the explanatory and response variables?
ﬁPhnam = Shel? Wammi' )7/(2 points) “ghat are ggexpensﬁigg‘gi units and how manyarethere? BoHom 6mm . v .
Maddlt W9 '5 dtﬁccnml/ Shalom? palm/1&8
as we ‘ ' (2 points) What type of experiment is this? '
B I‘ d) (2 points) Is there any indication that shelving policies have an effect on number of cans of soup sold? Explainin aﬁill sentence. , ‘
WeSﬁhere is on iﬂdicazh‘on +m+ shelving policies echd sales. when being placed on m medic shew +We Soup ma » _vaCi/\ h!5)h€f sales ~Hnan {)0 W 0" bow slaLIP.‘ I
2 . (7 points) A side effect of a certain anes etic used 1n surgery 1s the hiccups, which occurs in about 10 percent of the cases. Ifthree patients are scheduled for surgery today
and are to be administered this anesthetic, compute the following probabilities: a) (3 points) What is the probability that all three patients get hiccups?
g 0' Xv, YJ: aOO‘ ' a \K; (4 points) What is the probability that at least one patient gets hiccups? UK .IYB 2.5 1’: ‘ on my '
21. (11 points) Assuming that tﬁgwgebkly fooclﬁeii’tpeiil 'tures of families of a certain size in one economic group are approximately normally distributed with a mean of $130 and a
standard deviation of $20: a) (3 points) What proportion of the expenditures are less than $90? amen<3— :. _ .
5o+ Ll7.5 ‘00 ONE) 1)) (4 points) What percentage of the expenditures are either less than $120 or more thanSISO? 50__ (mg/7h : [10,60
50 34 7 l‘LO. I ‘ ml 0) (4 points) Above what value does the top 14 percen of the expenditures lie?
2293.16le y: \.0%’(’ZO)+\?>O : 22. (5 points) Every Normal model is deﬁned by its parameters: the mean and the
standard deviation. For the situation given below, ﬁnd the missing parameter. A tire manufacturer states that 20% of Brand 0 tires snow tires last 40,000 miles or more. If the standard deviation of Brand 0 tires is 0‘
u of the snow tires? 4.10, <54
2‘ ' Long Answer Questions (44 pints]:
23. (14 points) Listed in the stemplot below are the selling prices (in thousands of dollars) of a sample of 17 housing lots sold by agents working in Lucas County, Ohio.
For example, 1  3= $13,000 1 367
11 .‘o/ 2 05679
3
4
5 05
6 58
7
s 06
35 9 02
10
1 1
12 8 a) (2 points) Describe the shape of the distribution in detail.
Spme ‘ l 3pm ins/Jew ’
OUcHIYC =#118,ooo/ Gaps: 1 000— J o (omooo  €0,000, 012,000  123/000
b) (4 points) Determme the Sn ber summary for the data. —_ o
ﬂaanfgéigo 133+ 43 “191000
Qg— 831000 c) (2 points) Are there any outliers? Check for outliers using the criterion. (show
work ’4'), \€) 38,000 d) (4 points) Construct a boxplot of the data. Label your boxplot using the 5~number
summary. 10 20 30 4O 50 60 70 80 90 100 110 120 I30
(Values are thousands of dollars) e) (2 points) Describe both the differences and similarities between your boxplot and
your stemplot. Mosi of W data SEE/mg AoQtU 0L4: m \cmev numbefs in M Plat. W in W Slim » 8
PW“? spr ,“ié’mn , c» m M 5a. gap: m 544m @1099 24. (17 points) A market analyst is hired to provide information on the type of customers
who shop at a particular store. A random survey is taken of 100 shoppers at this store.
Of these 100, 73 are women. The sheppers are grouped in three age categories, under 30,
30 up to 50 and 50 and over. The data is summarized below. Let M be the event that a randomly selected shopper is a man.
Let Wbe the event that a randomly selected shopper is a woman.
Let A be the event that a randomly selected shopper is under 30.
Find the following probabilities: a) (2 points) P (Not HO '
P (Nor. N) 2.9“! 0( {flag ’ TS : 2.7 b) (2 points) P (A) 1:043:33 of 38970
c) (3 points) 'P (A andM) 0/“
PC“: and M) 3 .08 or 8 D d) (3 points)P(A or not W) ' 0V /
mt) + Pm) “P (a W t“
.35? .731  .08“ or 57570 e) (4 points) P (A  W)
7' p .3s.13)i4>(®) ’
38‘11—3) ' 913,7 :U'ogﬂaoﬁo
t) (1point)P(WandM) 7 4
p (,75.+.3") =Loﬂ ‘W" g) (2 points) What probability rule does this result In part 1) demonstrate? +ma+ an POSSbHHFlCS MUS d (Ab 4’0 CCU/(Obi LO Sf“ [00%, 25. (16 points) A major oil company is studying the relationship between the daily trafﬁc
count and the number of gallons of gasoline pumped at company stations. A sample of
eight company owned stations is selected and the following information obtained: Descriptive Statistics: Total Gallons, Trafﬁc Count Variable Mean StDev
Total Gallons j 133.8 45.3
Trafﬁc x; 4.500 1.927 RSquared = 97.8% a) (2 points) Find the correlation coefﬁcient from the descriptive statistics above. % r2.qu b) (2 points) Assuming the number of gallons of gasoline pumped is the response
variable, describe in one sentence the relationship between total gallons and
trafﬁc count. [ For over cum in claim +VCLQFiC, , A
@Qllons o? 8013 \5 pumped cu com:qu Sheena c) (5 points) Find the equation for the LeastSquares Regression Line showing all of
your work. ' d) (2 points) Predict the total number of gallons of gasoline pumped for a daily
trafﬁc count of 8 cars. (‘2:;_ 2" g7 aa‘i ,O‘i gallon: e) (3 points) The IlS has a daily trafﬁc count of 8 cars and the number of gallons of
gas pumped is 210. Calculate the residual for this observation using part (1) meve' a’oLl .Ool v a \O : 132%
r“ V
3 / f) (2 points) Is a linear model appropriate for this data? Explain using an
appropriate measure of predictive power. (2/4 Yes) 0L smear model is approprin because ~Hne£r iseems +0 be a. dimer reladricmshlp belwet/n Qauons
pumped omd rtvmcic, Commls. The Vadic—Pwe PCNUQV 0? (41.8470 0"“) i5 vet/5 stmrlg  10 [Z  ...
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