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Statistics                                                          Chapter 1-2 Test

1. A ______________ consists of all subjects that are being studied.

2. Which branch of statistics would buy a hundred Toyotas, drive them into the ground,
record the final mileage, and then write a report for Car and Driver?

A) predictive statistics
B) descriptive statistics
C) inferential statistics
D) differential statistics

3. Rating a restaurant by a number of stars is an example of an ordinal level of
measurement.

A) True
B) False

4. An ad for an exercise product states: "Using this product will burn 74% more calories."
This is an example of

A) changing the subject
B) detached statistics
C) suspect samples
D) ambiguous averages

5. What level of measurement classifies data into mutually exclusive (nonoverlapping),
exhausting categories in which no order or ranking can be imposed on the data?

A) nominal
B) ordinal
C) interval
D) ratio

6. The _______________ level of measurement classifies data into categories that can be
ranked; however, precise differences between the ranks do not exist.

7. What type of sampling is being employed if the country is divided into economic
classes and a sample is chosen from each class to be surveyed?

A) random sampling
B) systematic sampling
C) stratified sampling
D) cluster sampling
8. Inferential statistics is based on probability theory.

A) True
B) False

9. The amount of time needed to run the Boston marathon is an example of which type of
variable?

A) discrete
B) qualitative
C) continuous
D) none of the above

10. A ______________ variable assumes values that can be counted.

11. One advantage of a(n) ______________ study is that it occurs in a natural setting.

12. Which type of graph represents the data by using vertical bars of various heights to
indicate frequencies?

A) ogive
B) frequency polygon
C) histogram
D) cumulative frequency

13. The __________ is obtained by first adding the lower and upper limits and then
dividing by 2.

14. An automobile dealer wants to construct a pie graph to represent types of cars sold in
July. He sold 72 cars; 16 of which were convertibles. The convertibles will represent
how many degrees in the circle?

A) 60°
B) 80°
C) 100°
D) 50°

15. A Pareto chart arranges data from largest to smallest according to frequencies.

A) True
B) False
16. Graphs give a visual representation that enables readers to analyze and interpret data
more easily than they could simply by looking at numbers.

A) True
B) False

17. An ogive graph is also called a cumulative frequency graph.

A) True
B) False

18. The graphs that have their distributions as proportions instead of raw data as
frequencies are called

A) relative frequency graphs.
B) ogive graphs.
C) histograms.
D) frequency polygons.

19. Given the following frequency distribution, how many pieces of data were less than
28.5?

Class Boundaries       Frequencies
13.5–18.5              4
18.5–23.5              9
23.5–28.5              12
28.5–33.5              15
33.5–38.5              17

A) 12
B) 9
C) 25
D) 17
20-21. Using the following frequency distribution, construct a histogram.

Temperature            Frequency
28.5–31.5              1
31.5–34.5              3
34.5–37.5              6
37.5–40.5              10
40.5–43.5              8
43.5–46.5              7

22-23. A local fundraiser wants to graphically display the contributions they have
received over the past five years. Construct a time series graph for the following data.

Year           Contributions
1996           \$550
1997           \$700
1998           \$800
1999           \$1050
2000           \$1200

24-25. Construct a pareto chart using the following data from the local bakery.

Chocolate Chip              20
Peanut Butter               15
Oatmeal                     30
Sugar                       10
Statistics                                               Chapter 3 Test

The grades for a Trigonometry exam follow.

85, 76, 93, 82, 84, 90, 76

1. What is the range?
A) 84
B) 83.7
C) 76
D) 17

2. What is the mean?
A) 84
B) 83.7
C) 76
D) 17

3. What is the median?
A) 84
B) 83.7
C) 76
D) 17

4. What is the mode?
A) 84
B) 83.7
C) 76
D) 17

5. Find the mean of the following data:

No of Books Read in One Month                Frequency
1                                            15
2                                            10
3                                            7
4                                            1
A) 3
B) 3.7
C) 1.8
D) .9
6. Find the weighted mean for three exams if the first one was worth 75 points and the
student received a score of 70%, the second was worth 50 points and the student
received a score of 80% and the third was worth 30 points and the student received a
score of 95%?
A) 51.3
B) 85
C) 40.3
D) 78.1

7. Find the standard deviation of the following data set:

85, 76, 93, 82, 84, 90, 76
A) 83
B) 3.7
C) 6.4
D) 88.9

8. Find the standard deviation for the data set in question number 5.
A) 3
B) 3.7
C) 1.8
D) .9

9. Given that the mean of a set of data is 25 and the standard deviation is 3, what would
be the coefficient of variation?
A) 75%
B) 12%
C) 833%
D) 3.25%

10. Using Chebychev’s Theorem, what percentage of values will fall within 2 standard
deviations from the mean in a uniform distribution?
A) 75%
B) 68%
C) 88.89%
D) 95%

11. In a normal distribution, how many values will fall within 2 standard deviations from
the mean?
A) 75%
B) 68%
C) 88.89%
D) 95%
12. Find the z score for each student and indicate which one is higher.
Art Major X = 46       X = 50 s = 5
Theater Major X = 70 X = 75 s = 7

A) The art major has a higher score than the theater major.
B) The theater major has a higher score than the art major.
C) Both students have the same score.
D) Neither student received a positive score; therefore, the higher score cannot be
determined.

The following lists the number of announcements made by Mr. Morris for 9 days:

3, 1, 8, 9, 2, 1, 1, 7, 6

13. Find P60
A) 34
B) 6
C) 1
D) 45

14. What percentile does the 2 represent?
A) 34
B) 6
C) 1
D) 45

15. FindQ1 , Q2 , and Q3 for the following data set.
7, 21, 32, 38.
A) Q1 = 14, Q2 = 26.5, andQ3 = 35
B) Q1 = 10, Q2 = 25, andQ3 = 36
C) Q1 = 5, Q2 = 20, andQ3 = 39
D) Q1 = 14, Q2 = 25, and Q3 = 25

16. Which of the following is true?
A) D5=P5=Q5
B) D50 =P5 =Q25
C) D5=P50=Q2
D) D50 =P5 =Q2
17. Given the following boxplot where m is the median value, what statement could be

A) The distribution is approximately symmetric.

B) The distribution is positively skewed.

C) The distribution is negatively skewed.

D) No statement can be made about the data because no data values are shown on the
plot.

18. Which of the following symbols stands for the population mean?
A) s
B) σ
C) μ
D) x
19. Which of the following symbols stands for the population standard deviation?
A) s
B) σ
C) μ
D) x

20. Which of the following symbols stands for the sample mean?
A) s
B) σ
C) μ
D) x

21. Which of the following symbols stands for the sample standard deviation?
A) s
B) σ
C) μ
D) x
22-23. Calculate the standard deviation (σ) by hand.

5
3
7
2
4
12

X:                                                      /6            √

24-25. Give a 5 number summary for the following data and then make a box plot. Be
sure to include any outliers.

145, 119, 122, 118, 125, 116
Statistics                                                                     Chapter 5 Test
This Test is Worth 64 Points

1. Determine whether the following distribution is a probability distribution:

X                       2                       3                        7
P(x)                    .5                      .3                       .4

A) Yes
B) No

2. In order for a distribution to be a probability distribution, all probabilities must have a
value between _____ and _____, and the sum of all probabilities must be _____.

State whether Discrete or Continuous:

3. The number of drywall screws used in the basement of my current house.
A) Discrete
B) Continuous

4. The amount of water in the basement of my new house.
A) Discrete
B) Continuous

5. Calculate the mean of the following probability distribution:

X               0               1               2               3                4
P(x)            .18             .34             .23             .21              .04
A) .23
B) 1.1
C) 1.6
D) .9
6. Calculate the standard deviation of the probability distribution in problem 5.

A) .23
B) 1.1
C) 1.6
D) .9

7. Expected Value is the same thing as the __________.Find the standard deviation of
the following data set:

8. If a game is fair, the expected value is __________.

9. In a given card game it costs one dollar to play. If the player draws a 2 or a Jack, they
win \$10. Find the expected value.

A) win 53 cents
B) lose 53 sents
C) win \$28
D) lose \$28

10. An exit survey showed that 33% of the people who saw the movie “10,000 b.c.” this
past weekend said they would see it again. If we ask 12 people who watched the movie
this past weekend, what is the probability that exactly 4 would say they would see it
again?

A) .238
B) 1.1
C) 1.6
D) .231

11. Find P(x) given n = 12, x = 4, and p = .30 (Use table B on pg 716 of your textbook)

A) .23
B) 1.1
C) 1.6
D) .231
A restaurant study found that 24% of its patrons smoked. The seating capacity of the
restaurant is 80 people.

12. Find the mean

A) 4.38
B) 14.592
C) 3.81
D) 19.2

13. Find the standard deviation:

A) 4.38
B) 14.592
C) 3.81
D) 19.2

14. How many seats should be available in the smoking section of the restaurant?

A) 40
B) 20
C) 23
D) None, smoking is bad for you.

15-16. Construct a probability distribution for the data and draw a graph for the
distribution:

The probability that a patient will have 0, 1, 2, or 3 cavities on a visit to the dentist are
.18, .52, .21, and .09 respectively.
Chapter 6 Test                                           Name:_______________________

1 . What is the special property of the standard normal distribution?
A) The mean is 0 and the standard deviation is 1.
B) The total area under the normal distribution curve is equal to 1.00.
C) The curve is continuous.
D) The mean is located at the center of the distribution.

2. Which of the following properties does not apply to a theoretical normal distribution?
A) The normal distribution is bell-shaped.
B) The mean, median, and mode are equal.
C) The normal distribution is bimodal.
D) The curve never touches the x-axis.

3. Give the type of distribution pattern that occurs when the majority of the data values
fall to the left of the mean?
A) symmetrical
B) positively skewed
C) negatively skewed
D) left skewed

4. Give the term for the number of standard deviations that a particular X value is away
from the mean.
A) z value
B) discrete value
C) continuous value
D) y value

5. Find the area under the curve to the left of z = 1.69 .

A) 0.4545
B) 0.4452
C) 0.9545
D) 0.9452
6. In the figure below, what is the area under the curve between z = 1.50 and z = 2.50 ?

A) 0.0802
B) 0.0606
C) 0.0764
D) 1.00

7. What is the z value to the right of the mean such that 85% of the total area lies to the
left of it as shown in the figure below?

8. Using the normal distribution curve shown in the figure below, find the area under the
curve between z = 0 and z = −2.16 ?

A) –0.4821
B) 0.4821
C) –0.4846
D) 0.4846
9. A recent study found that the average life expectancy of a person living in Africa is 53
years with a standard deviation of 7.5 years. If a person in Africa is selected at random,
what is the probability that the person will die before the age of 65?
A) 94.52%
B) 82.89%
C) 94.95%
D) 88.49%

10. In order to be accepted into a top university, applicants must score within the top 5%
on the SAT exam. Given that the test has a mean of 1000 and a standard deviation of 200,
what is the lowest possible score a student needs to qualify for acceptance into the
university?
A) 1330
B) 1400
C) 1250
D) 1100

11. The average hourly wage of workers at fast food restaurants is \$6.50/hr with a
standard deviation of \$0.45. Assume that the distribution is normally distributed. If 10
fast food restaurant workers are selected at random, what is the probability that they earn
more than \$6.75/hr?
A) 28.77%
B) 27.64%
C) 42.07%
D) 3.92%

12. The average hourly wage of workers at a fast food restaurant is \$6.50/hr with a
standard deviation of \$0.45. Assume that the distribution is normally distributed. If a
worker at this fast food restaurant is selected at random, what is the probability that
the worker earns more than \$6.75?
A) 28.77%
B) 27.64%
C) 42.07%
D) 3.92%

13. The average age of a vehicle registered in the United States is 8 years, or 96 months.
If a random sample of 36 vehicles is selected, find the probability that the mean of their
age is between 98 and 100 months? Assume the standard deviation for the population is
15.
A) 66.67%
B) 15.71%
C) 63.47%
D) 75.82%
14. If a baseball player's batting average is 0.340 or 34%, find the probability that the
player will have a bad season and only score at most 60 hits in 200 times at bat?
A) 12.64%
B) 11.72%
C) 50.34%
D) 13.14%

15. At a large department store, the average number of years of employment for a cashier
is 5.7 with a standard deviation of 1.8 years. If an employee is picked at random, what is
the probability that the employee has worked at the store for over 10 years?
A) 49.16%
B) 99.16%
C) 0.84%
D) 0.54%

16. A magazine reported that 6% of American drivers read the newspaper while driving.
If 500 drivers are selected at random, find the probability that exactly 40 will admit to
A) 1.96%
B) 2.04%
C) 1.28%
D) 0.56%

17. The percentage of U.S. households with an online connection is 44.9%. In a random
sample of 420 households, what is the probability that fewer than 200 have online
connections?

A) 14.23%
B) .3577%
C) 85.77%
D) .1423%

18. Which of the following conditions are not characteristics of a binomial distribution?

A) There must be a fixed number of trials
B) The outcome for each trial must be dependent
C) Each experiment can have only two outcomes
D) The probability for success must remain the same for each trial
SHOW ALL WORK!!

19-20. Letter frequencies are analyzed by the Central Intelligence Agency in an attempt
to decipher intercepted messages. In standard English text, the letter e occurs with a
relative frequency of 0.130.

(A). Find the mean and standard deviation for the number of times the letter e will
be found on standard pages of 2600 characters. (Yes it will be normal.)

(B). In an intercepted message sent to Iraq, a standard page of 2600 characters is
found to have the letter e occurring 307 times. Is this unusual?

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