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Unformatted text preview: Chapter 7 Scatterplots, Association, and Correlation (Review) Name __..— MULTIPLE CHOKIE. Choose the one alternative that best completes the statement or answers the question. Suppose you were to collect data for the pair of given variables in order to make a scatterplot. Determine for each
variable if it is the explanatory variable, the response variable, or whether it could be both. 1) Studying consistently, high grade point average 1) A) Studying consistently: both
High grade point average: both B) Studying consistently: both
High grade point average: explanatory C) Studying consistently: explanatory
High grade point average: both D) Studying consistently: explanatory
High grade point average: response E) Studying consistently: response
High grade point average: explanatory 2.) Hot chocolate sales, heater sales 2) A) Hot chocolate sales: both
Heater sales: both B) Hot chocolate sales: explanatory
Heater sales: response C) Hot chocolate sales: response
Heater sales: explanatory D) Hot chocolate sales: explanatory
Heater sales: both E) Hot chocolate sales: both
Heater sales: explanatory 3) Adult: weight (pounds), adult: height (inches) 3) A) Adult: weight (pounds): both
Adult: height (inches): explanatory B) Adult: weight (pounds): explanatory
Adult: height (inches): both C) Adult: weight (pounds): response
Adult: height (inches): explanatory D) Adult: weight (pounds): both
Adult: height (inches): both E) Adult: weight (pormds): explanatory
Adult: height (inches): response Suppose you are to form a scatterplot by coilecting data for the given pair of variables. Determine the likely direction,
form, and strength. 4) Student: high grade point average, student: studying consistency 4)
A) Positive, straight, moderate
B) Positive, no form, strong
C) Positive, noniinear, moderate
D) Negative, straight, moderate E) Negative, nonlinear, moderate 5) Student: grade point average, student: height (feet) 5)
A) Negative, straight, moderate
B)'Positive, no form, very weak
C) No direction, linear, moderate
D) No direction, no form, very weak E) No direction, no form, strong 6) How tired you are, hours of sleep 6)
A) Positive, nonlinear, moderate
B) Negative, nonh'near, moderate
C) Negative, linear, moderate
D) Positive, linear, moderate E) Negative,noniinear, strong 7) Air pressure, attitude 7)
A) Positive, straight, moderate
B) Negative, straight, strong
C) Negative, nonlinear, strong
D) Negative, straight, moderate E) Positive, straight, strong Determine Whether the scatterplot shows iittie or no association, a negative association, a positive association, a iineaz
association, a moderately strong association, or a very strong association (multiple associations are possible). 8) 8) A) Linear association, moderately strong associatiOn
13) Linear association, very strong association C) Positive association, linear association D) Positive association, moderately strong association E) Positive association, iinear association, very strong association 9) 9) A) Negative association, moderately strong association
B) Positive association, linear association C) Little or no association D) Negative association, linear associatiOn E) Positive association, moderately strong associatiOn 10) 10) A) Linear association, very strong association 8) Negative association, linear association, very strong association
C) Negative association, moderately strong association D) Negative association, linear association E) Linear association, moderateiy strong association 11) 11) A) Linear association, moderately strong association
B) Linear association C) Positive association, moderately strong association
D} Positive association E) Positive association, moderateiy strong association, linear association 12) 12) A) Moderately strong association B) Linear association
C) Linear association, moderately strong association
D) Positive association, linear association E) Little or no association SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Draw the Specified histogram. 13) A ceramics factory can fire six large batches of pottery per day. Sometimes in the process a 13)
few of the pieces break. In order to understand the problem better, the factory records the
number of broken pieces in each batch for 4 days and then creates the scatterplot shown. Make a histogram showing the distribution of the number of broken pieces in the 24
batches of pottery examined. ﬁ Broke §ieces 1 Z 3 4 5 6
Batch Nowhex 14) Owners of a new computer store tracked sales (in thousands) for the ﬁrst 12 days, and 14)
displayed the data in a scatterplot. Make a histogram of the daily sales since the shop has been in business. 2 4 6 81012922}; 15) Data collected from 20 students in Statistics classes included their heights (in inches) and 15)
weights (in pounds), and are displayed in the following Scatterplot. Make a histogram of
the weights of the Children. 27%]
@243
3g72m
s 180
g 150 1 2'0
90 82 54 BE 58 m 3’2 F’B
Height (in) 16) A survey was conducted in 26 counties to determine the percentage of teenagers who had 16)
used marijuana and other drugs. Data are displayed in the foiiowing scatterplot. Make a
histogram of the other drugs. 0‘1
C3 D M
[3 Other Dwgs (026]
L33 bu
[:1 .4
D 1U 28 30 4C} 5%]
Marijuana (96) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question, Several scatterplots are given with calculated correlations. Which is which? 17) 1) 2) 17) r33
.v 3) a) '“0.928, b) w0.411, C) 0.002, (1)0711 A) 1b, 2c, 3d, 4a
8) 1d, Ea, 3b, 4c
C) 1c, 2a, 3d, 4::
D) 1c, 2d, 3a, 4b
B) 1a, 2b, 3c, 4d 18) 1) 3) a) —0.712, b) 0.001, c) 0.061, d) 0.916 A) 1d, 2a, 3b, 4c
8) 1b, 2c, 3a, 4:31
C) 1a, 2b, 3c, 4d
D) 1c, 2a, 3d, 4c:
E) 113, 2C, 3d, 4a SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Construct a scatterplot for the data. 19) The foilowing tabie gives the total sales (revenue) and profits for 8 retailers. 2) 4) Totai Sales Profits
Company (Millions of $) (Milﬁons of $)
Adams 57.0 2.2
Brown 15.0 0.8
Clay 45.0 2.6
Donner 27.5 0.9
Esters 64.0 3.0
Framer 35.0 1.8
Gillies 22.0 1.4 Ha s 9.5 0.5 [ 19) 18) 20) The table contains the daily study time for students from Statistics 101 and the grades on 20)
their quiz. Minutes on Grade on
Homework Quiz
45 S
60 10
65 9
35
50
50
10
15
35 {TINH‘JOO'Q 21) The table contains the weights (in pounds) and heights (in inches) of 9 randomly selected 21)
adults. Weight (lb) Height (in) 145 68
145 65
125 60
130 62
128 70
130 65
155 75
150 72
135 68
22) To get the best deal on a microwave oven, Amanda called six appliance stores and asked 22)
the cost and volume of several models. The prices and volumes she was quoted are listed below. Volume (cu.ft) Price ($) 1.5 22
0.7 49
1.5 349
1.9 183
0.5 119
2‘2 119
1.8 417
1.5 463
1 200 10 MGLTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the correlation. 23) The paired data below consist of the test scores of 6 randomly selected students and the number 03 hours they studied for the test. Hours Score A) —0.678 8) 0.224. C) 0.157 D) 0.678 s) w0.224 24) Two different tests are designed to measure empioyee productivity and dexterity. Severe}
empioyees are randomly selected and tested with these results. Productivity Dexterity 23 49
25 53
28 59
21 42
21 47
25 53
26 55
30 63
34 6'7
36 75
A) “0.280 13) 0.471 C) 0.159 D) 0.115 H) 0.986 25) A group of persons tilted in a questionnaire their age and the number of states they visited. The
resuits are recorded in the table below. Age States Visited A) 3.5 B) "3.5 C) 0.6 D) 4.7 E) —0.6 11 23) 24) 25) 26) The paired data below consist of the height of children (in inches) and their reading scores. Height (in) Reading Scores 4.6.75 62.9
51.25 67.9
48.75 64.9
52.25 71.9
52.75 72.9
54.25 75.9
47.75 64.9
55.25 76.9
A) 0.963 8) 0.985 C) 0.981 D) 0.943 E) 0.983
Solve the problem. 27) A science instructor assigns a group of students to investigate the reiationship between the pH 01
the‘water of a river and its water‘s hardness (measured in grains). Borne students wrote these conclusions: "there was a very strong correlation of1.47 between pH of the water and water's
hardness." Is the calculation of the correlation appropriate? A) No: correlation cannot be greater than 1.
B) Yes: correlation can be greater than 1.
C) No: correlation must be equal to I. D) No: there is little or no association. E) Yes: the pH and the hardness of the water are data collected from the same river. 28) A science instructor assigns a group of students to investigate the relationship between the pH oi
the water of a river and its water’s hardness (measured in grains). Some students wrote these conclusions: "there was a very strong correlation of 0.917 grains”1 between pH of the water and
water's hardness." Is the calculation of the correlation appropriate? A) No: there is little or no association. B) No: correlation has no units. C) Yes: correlation is less than 1. D) No: pH and hardness of water have different units. E) Yes: the pH and the hardness of the water are data coiiected from the same river. 29) A reporter investigates speeding on roads in a county and finds a correlation of0.942 between the
number of speeding tickets and the numbers of iniies of wellwpaved roads. Assuming that the
relation is linear, does it mean that there are more speeding tickets on well—paved roads? A) Yes: the correlation is close to 1. 13) Yes: the relation is linear. C) Yes: the two variables are quantitative. D) No: the correlation does not imply causality. E) No: Speeding is a categorical variable. 12 25) 27) 28) 2.9) 30) A shop owner tries to predict heater sales by displaying the sales of hot chocolate and heaters or 30)
the foilowing scatterplot. Does the scatterplot of hot chocoiate sales and heater sales indicate that it
is appropriate to calculate the correlation? Heater SaEes ($1038)
w: M to J: tIi ca «.3 1 2 3 it 5 E 3’
Hot Chocolate Sales ($10) A) Yes: the relation is strong. B) Yes: the relation is linear. C) Yes: the two variables are quantitative.
D) No: the relation must be linear. E) Yes: the direction is positive. 31) A survey was conducted in 20 counties to determine the percentage of teenagers who had used 31)
marijuana and other drugs. Data shown on the following scatterplot indicate a correlation (£0945
between the percent of teens who have used marijuana and the percent who have used other drugs.
Describe the association. 5E] 41.
D M
I3 Other Drugs (9’9)
8 .4
C3 10 20 3%] d0 58
Marijuana filo) A) No evidence of relation B) Weak linear relation in a positive direction C) Strong curved reiation in a positive direction
D) Strong nonlinear relation in a positive direction E) Strong linear relation in a positive direction 13 32) Almost all of the acidity of soda pop comes from the phosphoric acid which is added to give them a 32)
sharper ﬂavor. Is there a relation between the pH of the soda and the amount of phosphoric acid (in
grams)? The pH and phosphoric acid content of 12 ounces of several brands of soda are shown on
the following scatterplot. The correlation between pH and phosphoric acid is —G.964. Describe the
association. 5 10 15 2E! 25
Phosphoric Acid (133) A) Strong linear relation in a positive direction 8) No evidence of relation C) Weak linear relation in a negative direction D) Very strong linear relation in a negative direction E) Strong relation in a negative direction 33) Adam would like to buy a used car, and collected several data to evaluate the best model (such as 33)
age, price, weight, etc.) Thanks to a scatterplot, he established that the relation between age and
weight is somewhat linear. He calculated that the correlation between age and weight is 0.512.
Describe the association. A) No evidence of relation
B) Weak linear relation in a positive direction
C) Weak linear relation in a negative direction l3) Weak linear relation 13) Strong linear relation in a positive direction 34) In a school, a scientiﬁc observed children during lunch time over several months to study how 34)
much they eat and for how many minutes. He evaluated in calories what each child ate each day
for lunch. After careful observations, he found that the variables time and calories relate linearly,
and that the correlation between those variables is 0.633. Suppose he was to record time in hours
rather than in minutes. Would the correlation change? A) Yes: the two variables do not have the same units. B) No: the relation is linear. C) No: correlation changes with change of units. D) No: correlation does not change with change of units. E) Yes: correlation changes with change of units. 14 35) A clothes shop owner tries to predict the winter collection sales by displaying the coats sales (in 35)
dollars) and the Outside temperature (in degrees Fahrenheit) on the following Scatterplot. He
calculates that the correlation between coats sales and temperature is —D.755. Suppose the variable
temperature is recorded in degrees Celsius rather than in degrees Fahrenheit. What will be the
correlation? Coats Sales ($130)
we N [.53 4h 01 {In «4 “ES 2!] 38 40 ED 60 ?U
Temperature FF) A) 0.755
B) 0.755 C) 48.197 C°  e
D) 41755 c °/ e
E) 0755 c ° s3 36) The paired data below consist of the height (in inches) of children and their reading scores. If the 36)
height was recorded in centimeters, what would be the correlation? Height (in) Reading Scores 46 66
50.5 71
48 68
51.5 75
52 76
53.5 79
47 68
54.5 80
A) 0.387 13) 0.983 C) 41983 D) 2.497 E) 1.567 15 Find the lurking variable. 3'7) A researcher studies children in elementary school and finds a strong positive linear association
between shoe size and reading skiiis. Find the lurking variable, if there is one. A) Age B) Shoe brand C) School [3) Grade of students
E) No lurking variable 38) A teacher studied students' grades and established with a scatterplot a strong correlation betweer
SAT scores and college grades. Find the lurking variable, if there is one. A) IQ B) College C) Attendance D) High school E) No iurking variable 39) A study shows that the amount of chocolate consumed in Canada and the number of automobile
accidents is positively related. Find the lurking variable, if there is one. A) Population growth
B) Speed C) Children D) Vacation E) No lurking variable Previde an appropriate response.
40) All but one of these statements contain a blunder. Which could be true?
A) Triere is a high correlation (1.09) between height of a corn stalk and its age in weeks.
B) rI'here is a correlation of 0.63 between gender and political party.
C) The correlation between a car's length and its fuel efficiency is 0.71 miles per gailon.
D) The correlation between the amount of fertilizer used and the yield of beans is 0.42. E) The correlation between a football player's weight and the position he piays is 0.54. 16 37) 38) 39) 40) 41) All but one of the statements beiow contain a nﬁstake. Which one could be true? 41)
A) The correlation between weight and length of foot is 0.488.
B) The correlation between the breed of a dog and its weight is 0.435.
C) The correlation between height and weight is 0.568 inches per pound. D) If the correlation between blood alcohol level and reaction time is 0.73, then the correlation
between reaction time and blood alcohol level is —0.73. E) The correlation between gender and age is —0.171. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 42) Data show that there is a positive association between the population of 17 European 42)
countries and the number of stork pairs in those countries. Brieﬂy explain what "positive
association" means in this context. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the Question 43) All but one of the statements beiow contain a mistake. Which one could be true? 43)
A) The correlation between age and weight of a newborn baby is r = 0.83 ounces per day.
B) The correlation between the species of tree and its height is r= 0.56.
C) The correlation between blood alcohol level and reaction time is r= 0.73.
D) The correlation between a person’s age and vision (20/20?) is r = 4.04;. E) There is a high correlation between cigarette smoking and gender. 17 Answer Key
Testname: CHAPTER 7 SCATTERPLOTS, ASSOCIATION, AND CORRELATION (REVIEW) 1) 1:)
2) A
3) D
4) A
5) D
6) c
7) B
8) ":2
9) c
10) 13
11) E
12) A
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2 90 120150 188 2113240 230
Weight (lb) 18 Answer Key
Testname: CHAPTER 7 SCATTERPLOTS, ASSOCIATION, AND CORRELATION (REVIEW) 16)
7
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5 5
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Minutes on Hemework 19 Answer Key
Testname: CHAPTER 7 SCATTERPLOTS, ASSOCIATION, AND CORRELATION (REVIEW) CG
(:3 Height (in)
m :33 0a "4 “a:
(5'1 cm LI“! C3 U“: 11!] 12C! 13C] MD 159 180
Weight (lb)
22)
605
45E}
408
H 350
a 385]
g 259
E3— 208
150 18!]
50 3.5 3 1.5 2 2.5
Volume {00.11) 23) B
24) E
25) C
26) E
27) A
28) B
29) D
30) B
31) E
32) D
33) B
34) D
35) B
36) B
37) A
38) A
39) A
40) D
41) A
42) Positive association implies that courttries with larger popuiations tend to have more stork pairs and countries with smaller populations tend to have fewer Stork pairs.
43) C 20 ...
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 Spring '09
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