stat_review_test2_fall07.tst - TestGen

Review for Test 2: Statistics
∑(xi - x) 2
Note: s2 =
n-1
x 2 ∑xi
2
∑ i -
n
=
n-1
Also y^ = b1x + b0 where b1 = r · s y
sx
∑(xi - μ)2 ∑ x 2 i -
and σ2 =
=
N
N
and b 0 = y - b1x
∑xi
2
N
(Sections 2.2 through 5.2. Note that you will be given the formulas above on the test as well as this
review.)
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
1) A random sample of 30 high school students is selected. Each student is asked how much
time he or she spent watching television during the previous week. The following times
(in hours) are obtained:
1)
11, 19, 13, 16, 13, 11, 13, 12, 10, 16, 14, 12, 12, 11, 14, 13, 10, 10, 15, 12, 10, 12, 19, 14, 11, 15,
11, 14, 13, 12
Construct a frequency distribution for the data.
2) A random sample of 30 high school students is selected. Each student is asked how much
time he or she spent watching television during the previous week. The following times
(in hours) are obtained:
2)
6, 14, 8, 11, 8, 6, 8, 7, 5, 11, 9, 7, 7, 6, 9, 8, 5, 5, 10, 7, 5, 7, 14, 9, 6, 10, 6, 9, 8, 7
Construct a histogram for the data.
Construct a frequency distribution for the given data. Use the symbol -< to mean ʺup to, but not includingʺ.
3) Lori asked 24 students how many hours they had spent doing homework during the
previous week. The results are shown below.
3)
11 11 11 8 11 11 14 12 11 8 12 11
11 12 11 11 12 11 11 12 11 12 12 8
Construct a frequency table. Use 4 classes, a class width of 2 hours, and a lower limit of 8
for class 1. (Note that this data is continuous even though it has been rounded to a whole
number of hours.)
Hours Frequency
1

Provide the requested table entry.
4) The data in the following table reflect the amount of time 40 students in a section of
Statistics 101 spend on homework each day. Determine the value that should be entered in
the Relative Frequency column for the class 75-89. (Note that 0-

Provide an appropriate response.
6) Anna set up a grouped-data table with the following classes:
6)
Number of sick days taken
0-3
3-6
6-9
9-12
Frequency
What is wrong with these classes Describe two ways the classes could have been correctly
depicted.
Solve the problem.
7) The number of home runs that Mark McGwire hit in the first 13 years of his major league
baseball career are listed below. (Source: Major League Handbook)
7)
3 49 32 33 39 22 42 9 9 39 52 58 70
Make a stem-and-leaf plot for this data.
8) The Highway Patrol, using radar, checked the speeds (in mph) of 30 passing motorists at a
checkpoint. The results are listed below. Construct a dot plot for the data.
8)
44 38 41 50 36 36 43 42 49 48
35 40 37 41 43 50 45 54 39 38
50 41 47 36 35 40 42 43 48 33
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
9) Describe the shape of the distribution.
9)
A) skewed to the right B) uniform
C) symmetric D) skewed to the left
3

Use the histograms shown to answer the question.
10)
10)
Is either histogram symmetric
A) Neither is symmetric.
B) The first is symmetric, but the second is not symmetric.
C) Both are symmetric.
D) The second is symmetric, but the first is not symmetric.
A graphical display of a data set is given. State whether the distribution is (roughly) symmetric, right skewed, or left
skewed.
11) The ages of a group of patients being treated at one hospital for osteoporosis are summarized in
the frequency histogram below.
11)
A) Right skewed B) Symmetric C) Left skewed
4

Explain what is misleading about the graphic.
12)
12)
A) The horizontal scale does not begin at zero.
B) The graphic only includes information for one year.
C) The graphic may give the impression that drivers over age 65 had no DUIʹs in 2001.
D) The graphic is not misleading.
13)
13)
A) The horizontal label is incomplete.
B) The trend is depicted in the wrong direction.
C) The vertical scale does not begin at zero.
D) The graphic is not misleading.
5

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
14) A television manufacturer sold three times as many televisions in 1995 as it did in 1985. To
illustrate this fact, the manufacturer draws a pictogram as shown below. The television on
the right is three times as tall and three times as wide as the television on the left.
14)
Why is this pictogram misleading What visual impression is portrayed by the pictogram
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
15) A descriptive measure of a population is a
A) Qualitative response B) Statistic
C) Variable D) Parameter
15)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
16) The amounts of money won by the top ten finishers in a famous car race are listed below.
16)
$1,172,246 $163,659 $440,584 $350,634 $290,596
$186,731 $145,809 $143,209 $139,096 $125,106
Find the mean and median winnings. Round to the nearest dollar. Which measure - the
mean or the median- best represents the data Explain your reasoning.
6

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
17) The following data represent the bachelor degrees of CEOʹs at area small businesses. Determine
the mode degree.
17)
Degree Number
Accounting 22
Business 41
Liberal Arts 5
Marketing 29
Other 11
A) marketing B) accounting C) business D) no mode
18)
18)
For the distribution drawn here, identify the mean, median, and mode.
A) A = mode, B = mean, C = median B) A = mode, B = median, C = mean
C) A = median, B = mode, C = mean D) A = mean, B = mode, C = median
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Obtain the population standard deviation, σ, for the given data. Assume that the data represent population data. Round
your final answer to one more decimal place than that used for the observations. (Do this without using the statistical
package in the calculator.)
19) The normal annual precipitation (in inches) is given below for 8 different U.S. cities.
19)
9.0 7.0 6.3 13.0
19.4 6.8 10.2 17.6
Provide an appropriate response.
20) A group of medical researchers is interested in knowing the mean cholesterol level for all
men in the U.S. aged between 70 and 80. They pick a sample of 5,000 men and measure
their cholesterol levels. They then calculate the mean and standard deviation of these
cholesterol levels. Do the mean and standard deviation obtained in this way represent
parameters or statistics Why What symbols could you use to denote the mean and
standard deviation of the 5,000 cholesterol levels
20)
7

Solve the problem.
21) In a random sample, 10 students were asked to compute the distance they travel one way
to school to the nearest tenth of a mile. The data is listed below. Compute, by hand, the
range, sample standard deviation and sample variance of the data.
21)
1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8
Use the empirical rule to solve the problem.
22) The systolic blood pressure of 18-year-old women is normally distributed with a mean of
120 mmHg and a standard deviation of 12 mmHg. Approximately, what percentage of
18-year-old women have a systolic blood pressure that lies within 3 standard deviations
to either side of the mean
22)
Solve the problem.
23) A study was designed to investigate the effects of two variables - (1) a studentʹs level of
mathematical anxiety and (2) teaching method - on a studentʹs achievement in a
mathematics course. Students who had a low level of mathematical anxiety were taught
using the traditional expository method. These students obtained a mean score of 420 and
a standard deviation of 40 on a standardized test. Find and interpret the z-score of a
student who scored 460 on the standardized test.
23)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
24) The percentage of measurements that are above the 39th percentile is
A) 39% B) 61%
C) 71% D) cannot determine
24)
25) The weights (in pounds) of 30 preschool children are listed below. Find Q1. (Do not use the
statistical package in the calculator.)
25)
25 25 26 26.5 27 27 27.5 28 28 28.5
29 29 30 30 30.5 31 31 32 32.5 32.5
33 33 34 34.5 35 35 37 37 38 38
A) 27 B) 28 C) 38 D) 25
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
26) The weights (in pounds) of 30 preschool children are listed below. Find the interquartile
range of the 30 weights listed below. (Do not use the statistical package in the calculator.)
26)
25 25 26 26.5 27 27 27.5 28 28 28.5
29 29 30 30 30.5 31 31 32 32.5 32.5
33 33 34 34.5 35 35 37 37 38 38
8

27) The following is a sample of 19 test scores from a geography class:
52, 62, 66, 68, 72, 74, 74, 76, 76, 76, 78, 78, 82, 84, 84, 86, 88, 92, 96.
27)
Find the five-number summary. (Do this by hand. and show the steps.)
28) The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Draw a
modified boxplot that represents the data. (You can use a calculator and sketch the graph
below. Be sure that your scale is accurate.) Are there any outliers
28)
154 156 165 165 170 171 172 180 184 185
189 189 190 192 195 198 198 200 200 200
205 205 211 215 220 220 225 238 255 265
29) To study the physical fitness of a sample of 28 people, the data below were collected
representing the number of sit-ups that a person could do in one minute.
29)
10 12 12 15 15 15 18
20 22 25 25 26 29 30
32 33 40 40 40 45 46
47 48 48 50 52 53 56
Determine the lower and upper fences. Are there any outliers according to this criterion
(You may use a calculator to help. )
Solve the problem.
30) In an area of the Midwest, records were kept on the relationship between the rainfall (in
inches) and the yield of wheat (bushels per acre). Construct a scatter diagram for the data.
Determine whether there is a positive linear correlation, negative linear correlation, or no
linear correlation.
30)
Rain fall (in inches), x
Yield (bushels per acre), y
10.5
50.5
8.8
46.2
13.4
58.8
12.5
59.0
18.8
82.4
10.3
49.2
7.0
31.9
15.6
76.0
16.0
78.8
31) Construct a scatter diagram for the given data. Determine whether there is a positive
linear correlation, negative linear correlation, or no linear correlation.
31)
x
y
-5
11
-3
-6
4
8
1
-3
-1
-2
-2
1
0
5
2
-5
3
6
-4
7
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the scatter diagrams shown, labelled a through f to solve the problem.
9

32)
a
b
32)
12
y
12
y
10
10
8
8
6
6
4
4
2
2
1 2 3 4 5 6
x
1 2 3 4 5 6
x
c
d
12
y
12
y
10
10
8
8
6
6
4
4
2
2
1 2 3 4 5 6
x
1 2 3 4 5 6 7
x
e
f
12
y
12
y
10
10
8
8
6
6
4
4
2
2
1 2 3 4 5 6 7
x
1 2 3 4 5 6
x
In which scatter diagram is r = -1
A) f B) b C) d D) a
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
33) The data below are the ages and systolic blood pressures (measured in millimeters of
mercury) of 9 randomly selected adults. Calculate the correlation coefficient, r. (You can
use a calculator.)
33)
Age, x
Pressure, y
33
114
36
118
40
121
43
129
46
140
48
143
52
146
56
148
60
150
10

34) The data below are the temperatures on randomly chosen days during a summer class and
the number of absences on those days. Find the equation of the regression line for the
given data. (You can use a calculator.)
34)
Temperature, x
Number of absences, y
72
3
85
7
91
10
90
10
88
8
98
15
75
4
100
15
80
5
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
35) Is there a relationship between the raises administrators at State University receive and their
performance on the job
35)
A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y).
Consequently, the group considered the straight-line regression model
y^ = β0 + β1x.
Using the method of least squares, the faculty group obtained the following prediction equation:
Interpret the estimated y-intercept of the line.
y^ = 14,000 - 2,000x
A) For an administrator who receives a rating of zero, we estimate his or her raise to be $14,000.
B) For a 1-point increase in an administratorʹs rating, we estimate the administratorʹs raise to
increase $14,000.
C) The base administrator raise at State University is $14,000.
D) There is no practical interpretation, since rating of 0 is nonsensical and outside the range of
the sample data.
11

36) Is there a relationship between the raises administrators at State University receive and their
performance on the job
36)
A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y).
Consequently, the group considered the straight-line regression model
y^ = β0 + β1x.
Using the method of least squares, the faculty group obtained the following prediction equation:
Interpret the estimated slope of the line.
y^ = 14,000 - 2,000x
A) For an administrator with a rating of 1.0, we estimate his/her raise to be $2,000.
B) For a 1-point increase in an administratorʹs rating, we estimate the administratorʹs raise to
decrease $2,000.
C) For a $1 increase in an administratorʹs raise, we estimate the administratorʹs rating to
decrease 2,000 points.
D) For a 1-point increase in an administratorʹs rating, we estimate the administratorʹs raise to
increase $2,000.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
37) The data below are the final exam scores of 10 randomly selected statistics students and
the number of hours they studied for the exam. What is the best predicted value for y
given x = 8 (You can use a calculator to find the regression equation.)
37)
Hours, x
Scores, y
3
65
5
80
2
60
8
88
2
66
4
78
4
85
5
90
6
90
3
71
38) The regression line for the given data is y^ = 0.449x - 30.27.
38)
Temperature, x
Number of absences, y
72
3
85
7
91
10
90
10
88
8
98
15
75
4
100
15
80
5
Determine the residual of a data point for which x = 90 and y = 10.
39) Calculate the coefficient of determination, given that the linear correlation coefficient, r, is
0.837. What does this tell you about the explained variation and the unexplained variation
of the data about the regression line
39)
12

40) In a study of feeding behavior, zoologists recorded the number of grunts of a warthog
feeding by a lake in the 15 minute period following the addition of food. The data showing
the weekly number of grunts and and the age of the warthog (in days) are listed below:
40)
Number of Grunts Age (days)
88 123
66 139
37 153
42 158
61 165
38 172
60 181
15 187
18 193
Find and interpret the value of R2. (You may use a calculator to find R2.)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
41) Which of the following cannot be a probability
A) 0.001 B)
6
3
C) -55 D) 0
41)
42) Which of the following probabilities for the sample points A, B, and C could be true if A, B, and C
are the only sample points in an experiment
42)
A) P(A) = -1/4, P(B) = 1/2, P(C) = 3/4 B) P(A) = 1/4, P(B) = 1/4, P(C) = 1/4
C) P(A) = 0, P(B) = 1/14, P(C) = 13/14 D) P(A) = 1/8, P(B) = 1/7, P(C) = 1/10
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
43) Identify the sample space of the probability experiment: determining the childrenʹs gender
for a family of three children (Use B for boy and G for girl.)
43)
44) If sample points A, B, C, and D, are the only possible outcomes of an experiment, find the
probability of D using the table below.
44)
Sample Point A B C D
Probability 1/10 1/10 1/10
.
13

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
45)
45) The table below represents a random sample of the number of deaths per 100 cases for a certain
A) 1 35 ; 0.029 B) 35
; 0.35
100
35
C)
65 ; 0.538 D) 7
120 ; 0.058
illness over time. If a person infected with this illness is randomly selected from all infected people,
find the probability that the person lives 3-4 years after diagnosis.
Years after Diagnosis Number deaths
1-2 15
3-4 35
5-6 16
7-8 9
9-10 6
11-12 4
13-14 2
15+ 13
TRUE/FALSE. Write ʹTʹ if the statement is true and ʹFʹ if the statement is false.
Solve the problem.
46) The probability that event A will occur is
Number of successful outcomes
P(A) =
Total number of all possible outcomes
46)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
47) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of
getting a 2.
47)
Find the indicated probability.
48) A committee of three people is to be formed. The three people will be selected from a list
of five possible committee members. A simple random sample of three people is taken,
without replacement, from the group of five people. If the five people are represented by
the letters A, B, C, D, E, the possible outcomes are as follows.
48)
ABC
ABD
ABE
ACD
ACE
ADE
BCD
BCE
BDE
CDE
Determine the probability that C and D are both included in the sample.
14

List the outcomes comprising the specified event.
49) In a competition, two people will be selected from four finalists to receive the first and
second prizes. The prize winners will be selected by drawing names from a hat. The
names of the four finalists are Jim, George, Helen, and Maggie. The possible outcomes can
be represented as follows.
49)
JG JH JM GJ GH GM
HJ HG HM MJ MG MH
Here, for example, JG represents the outcome that Jim receives the first prize and George
receives the second prize. List the outcomes that comprise the following event.
A = event that Helen gets a prize
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
50) In 1999 the stock market took big swings up and down. A survey of 993 adult investors asked how
often they tracked their portfolio. The table shows the investor responses. What is the probability
that an adult investor tracks his or her portfolio daily
How frequently Response
Daily 231
Weekly 283
Monthly 280
Couple times a year 141
Donʹt track 58
A) 280
993
; 0.282 B)
141
993
50)
283
231
; 0.142 C) ; 0.285 D)
993 993 ; 0.233
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
51) The distribution of Masterʹs degrees conferred by a university is listed in the table.
(assume that a student majors in only one subject)
51)
Major Frequency
Mathematics 216
English 207
Engineering 92
Business 178
Education 217
What is the probability that a randomly selected student with a Masterʹs degree majored
in Business, Education or Engineering Round your answer to three decimal places.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
52) One hundred people were asked, ʺDo you favor the death penaltyʺ Of the 33 that answered ʺyesʺ
to the question, 14 were male. Of the 67 that answered ʺnoʺ to the question, six were male. If one
person is selected at random, what is the probability that this person answered ʺyesʺ or was a
male
52)
A) 0.53 B) 0.39 C) 0.13 D) 0.67
15

53) A sample of 280 shoppers at a large suburban mall were asked two questions: (1) Did you see a
television ad for the sale at department store X during the past 2 weeks (2) Did you shop at
department store X during the past 2 weeks The responses to the questions are summarized in the
table.
53)
Shopped at X Did Not Shop at X
Saw ad 135 40
Did not see ad 40 65
What is the probability that a randomly selected shopper from the 280 questioned did not shop at
department store X
A) 0.625 B) 0.143 C) 0.375 D) 0.232
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
List the outcomes comprising the specified event.
54) In a competition, two people will be selected from four finalists to receive the first and
second prizes. The prize winners will be selected by drawing names from a hat. The
names of the four finalists are Jim, George, Helen, and Maggie. The possible outcomes can
be represented as follows.
54)
JG JH JM GJ GH GM
HJ HG HM MJ MG MH
Here, for example, JG represents the outcome that Jim receives the first prize and George
receives the second prize. The events A and B are defined as follows.
A = event that Helen gets first prize
B = event that George gets a prize
List the outcomes that comprise the event (A or B).
16

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Describe the specified event in words.
55) When a quarter is tossed four times, 16 outcomes are possible.
55)
HHHH HHHT HHTH HHTT
HTHH HTHT HTTH HTTT
THHH THHT THTH THTT
TTHH TTHT TTTH TTTT
Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses
are tails, and the fourth toss is heads. The events A and B are defined as follows.
A = event exactly two tails are tossed
B = event the first toss is heads
Describe the event (A or B) in words.
A) Event that exactly two tails are tossed and the first toss is heads
B) Event that exactly two tails are tossed or the first toss is heads but not both
C) Event that exactly two tails are tossed or the first toss is heads or both
D) Event that the first toss is heads or the last two tosses are tails or both
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the indicated probability by using the special addition rule.
56) A percentage distribution is given below for the size of families in one U.S. city.
56)
Size Percentage
2 46.4
3 24.5
4 14.0
5 9.1
6 4.0
7+ 2.0
A family is selected at random. Find the probability that the size of the family is at most 3.
Round approximations to three decimal places.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
57) Given that P(A or B) = 1 2 , P(A) = 1 4 , and P(A and B) = 1 , find P(B).
9
57)
A) 13
36
B) 31
36
C) 23
36
D) 5 24
17

Solve the problem.
58) The following Venn diagram is for the six sample points possible when rolling a fair die. Let A be
the event rolling an even number and let B be the event rolling a number greater than 1.
58)
Which of the following events describes the event rolling a 1
A) B B) Ac C) Bc D) A ∪ B
59) In 5-card poker, played with a standard 52-card deck, 2,598,960 different hands are possible. If
there are 624 different ways a ʺfour-of-a-kindʺ can be dealt, find the probability of not being dealt
a ʺfour-of-a-kindʺ.
A)
624
2,598,960
B)
1248
2,598,960
C)
625
2,598,960
D) 2,598,336
2,598,960
59)
18

Answer Key
Testname: STAT_REVIEW_TEST2_FALL07
1)
Hours Number of
of TV HS Students
10 4
11 5
12 6
13 5
14 4
15 2
16 2
19 2
2) (Note that the bars are centered over the data values.)
Television Watching During a Week
3) (Note that 8-< 10 means all values from 8, including 8, up to 10 ,but not including 10. The same meaning is also used
for the other intervals.)
Hours Frequency
8-

Answer Key
Testname: STAT_REVIEW_TEST2_FALL07
5) Number of Days off in Year for Police Detectives
6) Answers will vary. Possible answer: In a grouped-data table, each observation must belong to one and only one class.
In Annaʹs table, there is overlap of the classes - it is not clear, for example, to which class the value 3 belongs. The
classes could have been depicted in either of the following ways:
7)
0 3 9 9
1
2 2
3 2 3 9 9
4 2 9
5 2 8
6
7 0
Number of sick days taken
0-

Answer Key
Testname: STAT_REVIEW_TEST2_FALL07
8)
9) A
10) A
11) C
12) C
13) C
14) Answers will vary. Possible answer: The area of the television on the right is nine times (not three times) the area of
the television on the left. The pictogram gives the visual impression that sales in 1995 were nine times the sales in
15) D
16) mean: $315,767; median: $175,195; the median
17) C
18) B
19) 4.72 in.
20) The mean and standard deviation represent statistics since they are descriptive measures for a sample. They are
denoted by x and s, respectively.
21) range = 4.4, s = 1.8, s2 = 3.324
22) 99.7%
23) The z-score is z = x - μ
σ .
460 - 420
For a score of 46, z = = 1.00.
40
This studentʹs score falls 1.00 standard deviations above the mean score of 420.
24) B
25) B
26) IQR = Q3 - Q1 = 34 - 28 = 6
27) 52, 72, 76, 84, 96
21

Answer Key
Testname: STAT_REVIEW_TEST2_FALL07
28)
29) lower fence = -22.25; upper fence = 87.75; outliers: none
30)
There appears to be a positive linear correlation between the variables.
31)
There appears to be no linear correlation.
32) D
33) 0.960
34) y^ = 0.449x - 30.27
35) A
36) B
37) 96
38) -0.14
22

Answer Key
Testname: STAT_REVIEW_TEST2_FALL07
39) The coefficient of determination, R2, = 0.701. That is, 70.1% of the variation is explained by the regression line for x
values and 29.9% of the variation is unexplained.
40) r2 = .627; Approximately 62.7% of the variation in the number of grunts is explained by age.
41) C
42) C
43) (BBB), (BBG), (BGB), (GBB), (BGG), (GBG), (GGB), (GGG)
44) 7/10
45) B
46) TRUE
47) 1 6
3
48)
10
49) JH, GH, HJ, HG, HM, MH
50) D
51) 0.535
52) B
53) C
54) JG, GJ, GH, GM, HJ, HG, HM, MG
55) C
56) 0.709
57) A
58) C
59) D
23