Statistics Midyear Exam Review
Mr. Lonergan/Mr. Yered
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
1) Define the terms population, sample, parameter and statistic. How does a census
compare to a sample?
1)
2) Define continuous and discrete data and give an example of each.
2)
3) Define observational study and experiment. Define the terms "treatment group" and
"placebo group" as part of your answer.
3)
4) Describe a double blind experiment and explain why blinding is used. Define the term
"placebo effect" as part of the answer.
4)
5) Define random sample. Explain why this is important in design of experiments.
5)
6) Define sampling error and nonsampling error. Give examples of nonsampling error.
6)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the given value is a statistic or a parameter.
7) A health and fitness club surveys 40 randomly selected members and found that the average
weight of those questioned is 157 lb.
A) Statistic
B) Parameter
Determine whether the given value is from a discrete or continuous data set.
8) The total number of phone calls a sales representative makes in a month is 425.
A) Discrete
B) Continuous
9) The height of 2-year-old maple tree is 28.3 ft.
A) Continuous
7)
8)
9)
B) Discrete
Determine whether the given description corresponds to an observational study or an experiment.
10) A clinic gives a drug to a group of ten patients and a placebo to another group of ten patients to
find out if the drug has an effect on the patients' illness.
A) Experiment
B) Observational study
11) A sample of fish is taken from a lake to measure the effect of pollution from a nearby factory on
the fish.
A) Observational study
B) Experiment
1
10)
11)
Provide an appropriate response.
12) An education expert is researching teaching methods and wishes to interview teachers from a
particular school district. She randomly selects ten schools from the district and interviews all of
the teachers at the selected schools. Does this sampling plan result in a random sample? Simple
random sample? Explain.
A) Yes; no. The sample is random because all teachers have the same chance of being
selected. It is not a simple random sample because some samples are not possible, such as
a sample that includes teachers from schools that were not selected.
B) Yes; yes. The sample is random because all teachers have the same chance of being
selected. It is a simple random sample because all samples have the same chance of being
selected.
C) No; yes. The sample is not random because teachers in small schools are more likely to be
selected than teachers in larger schools. It is a simple random sample because all samples
have the same chance of being selected.
D) No; no. The sample is not random because teachers in small schools are more likely to be
selected than teachers in larger schools. It is not a simple random sample because some
samples are not possible, such as a sample that includes teachers from schools that were
not selected.
13) The following frequency distribution analyzes the scores on a math test. Find the class
boundaries of scores interval 40-59.
Scores
40-59
60-75
76-82
83-94
95-99
A) 40.5, 58.5
A) 48.5
13)
Number of students
2
4
6
15
5
B) 39.5, 58.5
C) 39.5, 59.5
D) 40.5, 59.5
14) The following frequency distribution analyzes the scores on a math test. Find the class midpoint
of scores interval 40-59.
Scores
40-59
60-75
76-82
83-94
95-99
12)
Number of students
2
4
6
15
5
B) 49.5
C) 50.5
2
D) 49.0
14)
Construct the cumulative frequency distribution that corresponds to the given frequency distribution.
15)
Number
Weight (oz) of Stones
1.2-1.6
5
1.7-2.1
2
2.2-2.6
5
2.7-3.1
5
3.2-3.6
13
A)
B)
Weight (oz)
1.2-1.6
1.7-2.1
2.2-2.6
2.7-3.1
3.2-3.6
Cumulative
Frequency
5
7
12
17
30
C)
Weight (oz)
Less than 1.7
Less than 2.2
Less than 2.7
Less than 3.2
Less than 3.7
Cumulative
Frequency
5
7
12
17
30
Weight (oz)
Less than 1.7
Less than 2.2
Less than 2.7
Less than 3.2
Less than 3.7
Cumulative
Frequency
5
7
12
17
28
D)
Weight (oz)
Less than 2.2
Less than 3.2
Less than 3.7
Cumulative
Frequency
7
17
30
3
15)
Provide an appropriate response.
16) The frequency distribution for the weekly incomes of students with part-time jobs is given
below.
Construct the corresponding relative frequency distribution. Round relative frequencies to the
nearest hundredth of a percent if necessary.
Income ($) Frequency
200-300
60
301-400
73
401-500
91
501-600
89
More than 600
15
A)
Relative
Income ($) Frequency
200-300
27.33%
301-400
27.38%
401-500
4.60%
501-600
18.07%
More than 600
27.41%
C)
Relative
Income ($) Frequency
201-300
15.5%
301-400
22.1%
401-500
31.3%
501-600
16.2%
More than600
14.9%
B)
Relative
Income ($) Frequency
200-300
12.5%
301-400
20.1%
401-500
37.3%
501-600
15.2%
More than 600
14.9%
D)
Relative
Income ($) Frequency
200-300
18.29%
301-400
22.26%
401-500
27.74%
501-600
27.13%
More than 600
4.57%
4
16)
17) A nurse measured the blood pressure of each person who visited her clinic. Following is a
relative-frequency histogram for the systolic blood pressure readings for those people aged
between 25 and 40. The blood pressure readings were given to the nearest whole number.
Approximately what percentage of the people aged 25-40 had a systolic blood pressure reading
between 110 and 119 inclusive?
A) 30%
B) 0.35%
C) 3.5%
D) 35%
18) A nurse measured the blood pressure of each person who visited her clinic. Following is a
relative-frequency histogram for the systolic blood pressure readings for those people aged
between 25 and 40. The blood pressure readings were given to the nearest whole number. What
class width was used to construct the relative frequency distribution?
A) 11
B) 100
C) 10
5
17)
D) 9
18)
Construct the dotplot for the given data.
19) Attendance records at a school show the number of days each student was absent during the
year. The days absent for each student were as follows.
0 2 3 4 2 3 4 6 7 2 3 4 6 9 8
A)
B)
C)
D)
Use the pie chart to solve the problem.
20) The pie chart shows the percent of the total population of 73,700 of Springfield living in the
given types of housing. Round your result to the nearest whole number.
39%
19)
20)
32%
5%
7%
17%
Find the number of people who live in duplexes.
A) 3685 people
B) 70,015 people
C) 5 people
D) 0 people
Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place
than is present in the original data values.
21) The weights (in pounds) of six dogs are listed below. Find the mean weight.
21)
17 56 85 38 138 98
A) 71.5 lb
B) 72 lb
C) 86.4 lb
D) 72.5 lb
6
Find the median for the given sample data.
22) A store manager kept track of the number of newspapers sold each week over a seven-week
period. The results are shown below.
80 39 214 152 264 239 232
Find the median number of newspapers sold.
A) 152 newspapers
C) 232 newspapers
B) 214 newspapers
D) 174 newspapers
Find the mode(s) for the given sample data.
23) The speeds (in mi/h) of the cars passing a certain checkpoint are measured by radar. The results
are shown below.
41.3 43.7 44.9 41.8 45.5
45.5 43.7 40.9 47.9 41.8
41.3 40.9 41.8 39.5 43.7
44.3 44.3 44.9 49.7 41.3
A) 42.27
B) 41.3
C) 43.7
D) 41.3, 41.8, 43.7
Find the midrange for the given sample data.
24) 49 52 52 52 74 67 55 55
A) 61.5
B) 53.5
23)
24)
C) 12.5
D) 25
Find the mean of the data summarized in the given frequency distribution.
25) The highway speeds of 100 cars are summarized in the frequency distribution below. Find the
mean speed.
Speed (mph) Cars
30-39
4
40-49
19
50-59
50
60-69
15
70-79
12
A) 54.5 mph
22)
B) 58.5 mph
C) 55.7 mph
D) 61.3 mph
Solve the problem.
26) A student earned grades of 92, 79, 93, and 74 on her four regular tests. She earned a grade of 79
on the final exam and 88 on her class projects. Her combined homework grade was 87. The four
regular tests count for 40% of the final grade, the final exam counts for 30%, the project counts
for 10%, and homework counts for 20%. What is her weighted mean grade? Round to one
decimal place.
A) 83.7
B) 85.0
C) 84.5
D) 84.6
Find the range for the given sample data.
27) Jorge has his own business as a painter. The amounts he made in the last five months are shown
below.
$2416 $2423 $1644 $2036 $1267
A) $1156
B) $772
C) $779
D) $1149
7
25)
26)
27)
Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present
in the original data.
28) The top nine scores on the organic chemistry midterm are as follows.
28)
66, 43, 86, 45, 68, 62, 29, 62, 90
A) 7.7
B) 19.8
C) 18.7
D) 21.2
Find the standard deviation of the data summarized in the given frequency distribution.
29) The test scores of 40 students are summarized in the frequency distribution below. Find the
standard deviation.
Score Students
50-59
5
60-69
13
70-79
5
80-89
8
90-99
9
A) 14.7
B) 14
C) 13.3
D) 12.6
Use the empirical rule to solve the problem.
30) 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. What percentage of 18-year-old women have a
systolic blood pressure between 96 mmHg and 144 mmHg?
A) 99.99%
B) 99.7%
C) 68%
D) 95%
Solve the problem. Round results to the nearest hundredth.
31) The mean of a set of data is 5.73 and its standard deviation is 3.44. Find the z score for a value of
13.87.
A) 2.13
B) 2.61
C) 2.37
D) 2.67
Find the number of standard deviations from the mean. Round your answer to two decimal places.
32) The annual snowfall in a town has a mean of 38 inches and a standard deviation of 10 inches.
Last year there were 63 inches of snow. How many standard deviations from the mean is that?
A) 0.44 standard deviations below the mean
B) 2.50 standard deviations below the mean
C) 0.44 standard deviations above the mean
D) 2.50 standard deviations above the mean
29)
30)
31)
32)
Determine which score corresponds to the higher relative position.
33) Which score has a higher relative position, a score of 327.6 on a test for which x = 280 and s = 28,
33)
or a score of 22.2 on a test for which x = 20 and s = 2?
A) Both scores have the same relative position.
B) A score of 327.6
C) A score of 22.2
34) Which is better: a score of 82 on a test with a mean of 70 and a standard deviation of 8, or a score
of 82 on a test with a mean of 75 and a standard deviation of 4?
A) The first 82
B) The second 82
C) Both scores have the same relative position.
8
34)
Answer the question.
35) Which of the following cannot be a probability?
A) 1
B) 0
2
35)
C) 1
D) -1
36) Which of the following cannot be a probability?
A) 5
B) 3
3
5
C) 1
2
D) 2
3
37) What is the probability of an impossible event?
A) 0.1
B) 1
C) -1
D) 0
36)
37)
Find the indicated probability.
38) On a multiple choice test, each question has 5 possible answers. If you make a random guess on
the first question, what is the probability that you are correct?
A) 1
B) 1
C) 0
D) 5
5
38)
39) If a person is randomly selected, find the probability that his or her birthday is in May. Ignore
leap years.
A) 1
B) 31
C) 1
D) 1
365
365
31
12
39)
40) A class consists of 66 women and 98 men. If a student is randomly selected, what is the
probability that the student is a woman?
A) 33
B) 49
C) 33
D) 1
49
82
82
164
40)
Answer the question.
41) In a certain town, 25% of people commute to work by bicycle. If a person is selected randomly
from the town, what are the odds against selecting someone who commutes by bicycle?
A) 3 : 1
B) 3 : 4
C) 1 : 4
D) 1 : 3
Find the indicated complement.
42) Find P(A), given that P(A) = 0.732.
A) 1.366
B) 0
41)
42)
C) 1.732
D) 0.268
Find the indicated probability.
43) A spinner has equal regions numbered 1 through 21. What is the probability that the spinner
will stop on an even number or a multiple of 3?
A) 10
B) 1
C) 2
D) 17
9
3
3
9
43)
44) The manager of a bank recorded the amount of time each customer spent waiting in line during
peak business hours one Monday. The frequency table below summarizes the results.
44)
Waiting Time Number of
(minutes) Customers
0-3
11
4-7
9
8-11
11
12-15
5
16-19
5
20-23
1
24-27
3
If we randomly select one of the customers represented in the table, what is the probability that
the waiting time is at least 12 minutes or between 8 and 15 minutes?
A) 0.667
B) 0.727
C) 0.111
D) 0.556
45) A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing a face card or a 4).
A) 2
B) 4
C) 16
D) 12
13
13
13
45)
46) In one town, 39% of all voters are Democrats. If two voters are randomly selected for a survey,
find the probability that they are both Democrats. Round to the nearest thousandth if necessary.
A) 0.152
B) 0.390
C) 0.148
D) 0.780
46)
47) A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and
30% are defective. If three of the products are randomly selected, find the probability that all of
them are acceptable.
A) 2.1
B) 0.027
C) 0.429
D) 0.343
47)
48) A study conducted at a certain college shows that 51% of the school's graduates find a job in
their chosen field within a year after graduation. Find the probability that 5 randomly selected
graduates all find jobs in their chosen field within a year of graduating. Round to the nearest
thousandth if necessary.
A) 0.068
B) 2.550
C) 0.035
D) 0.098
48)
49) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing
cards. Find the probability that both cards are black. Express your answer as a simplified
fraction.
A) 1
B) 25
C) 25
D) 13
2,652
51
102
51
49)
50) A IRS auditor randomly selects 3 tax returns from 45 returns of which 15 contain errors. What is
the probability that she selects none of those containing errors? Round to four decimal places.
A) 0.2861
B) 0.2963
C) 0.0321
D) 0.037
50)
10
51) The table below describes the smoking habits of a group of asthma sufferers.
Light Heavy
Nonsmoker smoker smoker Total
Men
356
50
36
442
Women
418
43
45
506
Total
774
93
81
948
51)
If two different people are randomly selected from the 948 subjects, find the probability that
they are both heavy smokers. Round to six decimal places.
A) 0.0001524
B) 0.007301
C) 0.007218
D) 0.001442
52) A sample of 4 different calculators is randomly selected from a group containing 46 that are
defective and 26 that have no defects. What is the probability that all four of the calculators
selected are defective? Round to four decimal places.
A) 0.1021
B) 0.1666
C) 0.1586
D) 10.9154
Find the indicated probability. Round to the nearest thousandth.
53) A study conducted at a certain college shows that 55% of the school's graduates find a job in
their chosen field within a year after graduation. Find the probability that among 7 randomly
selected graduates, at least one finds a job in his or her chosen field within a year of graduating.
A) 0.143
B) 0.550
C) 0.985
D) 0.996
Solve the problem.
54) The library is to be given 3 books as a gift. The books will be selected from a list of 16 titles. If
each book selected must have a different title, how many possible selections are there?
A) 560
B) 48
C) 3360
D) 4096
52)
53)
54)
55) A state lottery involves the random selection of six different numbers between 1 and 25. If you
select one six number combination, what is the probability that it will be the winning
combination?
1
1
1
A)
B)
C)
D) 1
127,512,000
177,100
244,140,625
720
55)
56) A tourist in France wants to visit 12 different cities. How many different routes are possible?
A) 39,916,800
B) 144
C) 12
D) 479,001,600
56)
57) In a certain lottery, five different numbers between 1 and 20 inclusive are drawn. These are the
winning numbers. To win the lottery, a person must select the correct 5 numbers in the same
order in which they were drawn. What is the probability of winning?
1
120
A) 1
B)
C) 1
D)
20!
1,860,480
120
1,860,480
57)
11
Find the mean of the given probability distribution.
58) In a certain town, 40% of adults have a college degree. The accompanying table describes the
probability distribution for the number of adults (among 4 randomly selected adults) who have
a college degree.
x
P(x)
0 0.1296
1 0.3456
2 0.3456
3 0.1536
4 0.0256
A) µ = 2.00
B) µ = 1.50
C) µ = 1.60
D) µ = 1.73
Provide an appropriate response. Round to the nearest hundredth.
59) In a certain town, 40% of adults have a college degree. The accompanying table describes the
probability distribution for the number of adults (among 4 randomly selected adults) who have
a college degree. Find the standard deviation for the probability distribution.
x
P(x)
0
0.1296
1 0.3456
2 0.3456
3 0.1536
4
0.0256
A) σ = 1.88
B) σ = 0.96
C) σ = 1.12
D) σ = 0.98
Provide an appropriate response.
60) Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for
rolling a 1 or a 6, nothing otherwise. What is your expected value?
A) -$1.33
B) -$3.00
C) $3.00
D) $5.00
61) Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one
winning ticket is to be $500. What is your expected value?
A) -$0.50
B) $0.00
C) -$0.40
D) -$1.00
Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
62) Choosing 10 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time
without replacement, keeping track of the number of red marbles chosen.
A) Procedure results in a binomial distribution.
B) Not binomial: the trials are not independent.
C) Not binomial: there are too many trials.
D) Not binomial: there are more than two outcomes for each trial.
63) Choosing 8 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time with
replacement, keeping track of the colors of the marbles chosen.
A) Not binomial: there are more than two outcomes for each trial.
B) Procedure results in a binomial distribution.
C) Not binomial: the trials are not independent.
D) Not binomial: there are too many trials.
12
58)
59)
60)
61)
62)
63)
64) Choosing 10 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time with
replacement, keeping track of the number of red marbles chosen.
A) Not binomial: there are too many trials.
B) Procedure results in a binomial distribution.
C) Not binomial: there are more than two outcomes for each trial.
D) Not binomial: the trials are not independent.
Find the indicated probability.
65) In a survey of 300 college graduates, 53% reported that they entered a profession closely related
to their college major. If 9 of those survey subjects are randomly selected without replacement
for a follow-up survey, what is the probability that 3 of them entered a profession closely
related to their college major?
A) 0.135
B) 0.865
C) 0.149
D) 0.0512
66) Suppose that 11% of people are left handed. If 8 people are selected at random, what is the
probability that exactly 2 of them are left handed?
A) 0.337
B) 0.168
C) 0.0416
D) 0.0121
Find the indicated probability. Round to three decimal places.
67) An airline estimates that 97% of people booked on their flights actually show up. If the airline
books 70 people on a flight for which the maximum number is 68, what is the probability that
the number of people who show up will exceed the capacity of the plane?
A) 0.649
B) 0.257
C) 0.375
D) 0.119
13
64)
65)
66)
67)
Answer Key
Testname: STATISTICSMIDYEARREVIEW
1) A population is the complete collection of all elements. A sample is a subset of elements drawn from a population.
A parameter is a numerical measurement describing some characteristic of a population. A statistic is a numerical
measurement describing some characteristic of a sample. A census is the collection of data from every element in a
population; a sample is a subset of a population.
2) Continuous numerical data result from infinitely many possible values that can be associated with points on a
continuous scale so that there are no gaps or interruptions. Discrete data result from either a finite number of
possible values or a countable number of possible values. Examples will vary.
3) In an observational study, we observe and measure specific characteristics, but we don't attempt to manipulate or
modify the subjects being studied. In an experiment we apply some treatment and then proceed to observe its
effects on the subjects. In the experiment, the group receiving the treatment is called the treatment group. The
placebo group is the group that is not given the treatment.
4) A double blind experiment is one in which neither the subjects nor the researchers know who is getting the
treatment. Blinding is when the subject does not know whether he or she is receiving a treatment or a placebo.
Blinding is used to counteract the placebo effect in which an untreated subject believes he or she is receiving a
treatment and reports an improvement in symptoms due to this belief.
5) In random sampling, each member of the population has an equal chance of being selected. Random sampling
provides us with the best representative sample in which all groups of the population are approximately
proportionately represented. Careless sampling can easily result in a biased sample which may be useless.
6) Sampling error is the difference between a sample result and the true population result. Such an error results from
chance sample fluctuations. A nonsampling error occurs when the sample data are incorrectly collected, recorded,
or analyzed. Examples include nonrandom samples, defective measuring instruments, biased survey questions, a
large number of refusals, copying sample data incorrectly.
7) A
8) A
9) A
10) A
11) A
12) A
13) C
14) B
15) B
16) D
17) D
18) C
19) C
20) A
21) B
22) B
23) D
24) A
25) C
26) A
27) A
28) B
29) B
30) D
31) C
32) D
33) B
14
Answer Key
Testname: STATISTICSMIDYEARREVIEW
34) B
35) D
36) A
37) D
38) B
39) B
40) C
41) A
42) D
43) C
44) D
45) B
46) A
47) D
48) C
49) C
50) A
51) C
52) C
53) D
54) A
55) B
56) D
57) B
58) C
59) D
60) A
61) A
62) B
63) A
64) B
65) A
66) B
67) C
15