Statistics – Semester 1 Review
Proficiency 1-1 – Data Collection - Vocabulary
Classify each variable as qualitative or quantitative.
1. Weight of students in the class.
2. Amount of calories in a sandwich.
3. Month you were born.
Identify the type of sampling used.
4. A researcher randomly selects 5 of the 70 hospitals in a metropolitan area and then surveys all of the surgical doctors in
each hospital.
5.
A researcher segments the population of car owners into four groups: Ford, General Motors, Chrysler, and foreign. She
obtains a random sample from each group and conducts a survey.
6.
An interviewer is seeking peoples input on a recent sale in the mall and is told to survey every fifth shopper, starting with
the second.
7.
A list of students in elementary statistics is obtained in which the individuals are numbered 1 to 540. A professor randomly
selects 30 of the students.
Ten runners in the Olympics had their lung capacity measured one hour before their competition and measured again
immediately after the competition.
8. What is the response variable in this experiment?
9. What is the treatment?
10. What type of experimental design is this?
11. Identify the experimental units.
12. What are the three types of experimental designs?
Proficiency 1-2 – Organizing & Summarizing Data – Graphing Data
13. Retailers are always interested in determining why a customer selected their store to make
a purchase. A sporting goods retailer conducted a customer survey to determine why its
customers shopped at the store. The results are shown here. What percentage of the
customers responded that the merchandise was the reason they shopped at the store?
14. The circle graph to the right shows the results of the student council presidential election. What
percent of the votes did Jim and Gina receive together?
15. Describe the shape of each distribution.
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Statistics – Semester 1 Review
16. What is misleading about each graphic?
Proficiency 1-3 – Numerically Summarizing Data
17. Find the mean and standard deviation for the following data which represents the flight time (in minutes) of a random
sample of seven flights from Las Vegas, Nevada, to Newark, New Jersey, on Continental Airlines: 282, 270, 260, 266, 257,
260, 267
18. A researcher wanted information about the number of births that occurred on Mondays. Find the mean and stamdard
deviation of the data he collected which represents the number of births that occurred on a Monday during the first six
weeks of 1997.
10,456
10,267
10,444
10,527
10,596
10,778
19. A biologist measures the pH level of rain in Pierce County, Washington for a random sample of 19 rain dates and obtains
the following data:
5.08
4.78
4.79
5.03
4.73
4.66
5.00
4.65
4.78
5.05
4.70
4.50
4.91
4.77
4.70
4.87
4.73
5.07
4.60
Compute the z-score corresponding to 5.08.
20. The following data represent the number of inches of rain in Chicago, Illinois, during the month of April for 20 randomly
selected years: 2.47
1.14
5.22
3.48
6.28
3.97
4.02
0.97
4.77
5.50
3.94
3.41
6.14
2.78
7.69
4.11
1.85
2.34
4.00
5.79
Compute the z-score corresponding to 0.97.
21. Approximate the mean and the standard deviation for the following data which represents the number of people aged 2565 covered by health insurance in 1998.
Age
25-35
35-45
45-55
55-65
Number
(in millions)
28.5
35.7
26.2
14.9
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Statistics – Semester 1 Review
22. Approximate the mean and the standard deviation for the following data which represents the high temperatures for the
month of August in Chicago since 1972.
Temperature
50-60
60-70
70-80
80-90
90-100
100-110
Days
1
308
1519
1626
503
11
23. The amount of television viewed by today’s youth is of primary concern to Parents Against Watching Television (PAWT).
300 parents of elementary school-aged children were asked to estimate the number of hours per week that their child
watched television. The mean was 15 and the standard deviation was 1.8 for their responses. PAWT constructed a stemand-leaf display for the data that showed that the distribution of times was a bell-shaped distribution.
a. Draw the normal curve for this distribution
Give an interval where you believe approximately
b. 68% of the television viewing times fell in the distribution.
c.
95% of the television viewing times fell in the distribution.
d. 99.7% of the television viewing times fell in the distribution.
Proficiency 1-4 – Describing the Relation Between Two Variables – Bi-Variate Data
24. The data below displays the number of represents several states have.
State
AL
FL
IN
KY
LA
NC
Populition
4.0
12.9
5.5
3.7
4.2
6.6
(millions)
Representatives
7
23
10
6
7
12
a.
OK
SC
TN
VA
3.1
3.5
4.9
6.2
6
6
9
11
Find the equation of the least-squares
regression line for the given data.
b. What is the predicted value for y given
𝑥 = 7.1?
c.
What is the residual for the for the point
(7.1, 14)?
d. Find the correlation coefficient for the data.
e.
What is the coefficient of determination?
f.
Compute the sum of the squared residuals
of the regression line.
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Statistics – Semester 1 Review
25. In an effort to measure the dependence of energy expenditure on body build, researchers used underwater weighing
techniques to determine the fat-free body mass for seven men. In addition, they measured the total 24-hour energy
expenditure during inactivity. The results are shown in the table.
Fat-free Mass (kg)
49.3
59.3
68.3
48.1
57.6
78.1
76.1
Energy Expenditure (Kcal)
1894
2050
2353
1838
1948
2528
2568
a. Find the equation of the least-squares
regression line for the given data.
b. What is the predicted value for y given
𝑥 = 52.4?
c.
What is the residual for the for the point
(52.4, 1823)?
d. Find the correlation coefficient for the data.
e.
What is the coefficient of determination?
f.
Compute the sum of the squared residuals
of the regression line.
Proficiency 1-5 – Probability
26. The data in the table represent the marital status of males and females 18 years old or older in the United States in 1998.
Males (millions) Females (millions)
Never Married
25.5
21.0
Married
58.6
59.3
Widowed
2.6
11.0
Divorced
8.3
11.1
a. If a person is chosen at random, find the probability of getting someone who is a female or widowed.
b. What is the probability that a person is male given that he is married?
c.
What is the probability that a person has not been married?
27. The table lists the smoking habits of a group of college students.
a.
If a student is chosen at random, find the probability of getting someone who is a man or a non-smoker.
b. What is the probability that a person is a man and a non smoker?
c.
What is the probability that a person is female given that she is a heavy smoker?
d. What is the probability that a person is a smoker?
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Statistics – Semester 1 Review
28. Two members from a five-member committee are to be randomly selected to serve as chairperson and secretary. The first
person selected is the chairperson and the second person selected is the secretary. The members of the committee are
Bob, Faye, Elena, Melody, and Dave. Determine the probability that Elena is chairperson and Dave is secretary.
29. CampusFest is a student festival where local businesses come on campus to sell their goods to students at vastly reduced
prices. As part of a give-away promotion, a local electronics store gave away 200 iPods to students. Unbeknownst to the
company is that 22 of these iPods are defective. Suppose you and your roommate each received one of the giveaway
iPods. Find the probability that both of them are defective.
30. The table represents scores received on the 2000 SAT I: Reasoning Test – Verbal, by gender.
What is the probability that a randomly selected female scored 750-800 on the SAT?
31. A shipment of 120 fasteners that contains 4 defective fasteners was sent to a manufacturing plant. The quality-control
manager at the manufacturing plant randomly selects five fasteners and inspects them. What is the probability that exactly
one of the fasteners is defective?
32. A committee consisting of 8 people is to be selected from twelve parents and seven teachers. Find the probability of
selecting five parents and three teachers.
Proficiency 1-6 (Discrete Probability Distributions)
33. According to Nielsen Media Research, 75% of all United States households have cable television.In a random sample of 15
households, what is the probability that:
a. Exactly 10 have cable?
b.
At least 13 have cable?
c.
Fewer than 13 have cable?
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Statistics – Semester 1 Review
34. According the Crime in the United States, 1998, 65% of murders are committed with a firearm. Suppose 15 murders are
randomly selected. Find the probability that:
a. Exactly 13 murders are committed with a firearm
b. 13 or more murders are committed with a firearm
c.
12 or fewer murders are committed with a firearm.
35. Historically, a McDonald’s manager knows that cars arrive at the drive-through at the rate of 2 cars per minute between the
hours of 12 noon and 1:00 P.M. She needs to determine and interpret the probability of the following events:
a. Exactly 6 cars arrive between 12 noon and 12:05 P.M
b. At least 6 cars arrive between 12 noon and 12:05 P.M.
36. The number of hits to a Web site occur at the rate of 1.4 per minute between 7:00pm and 9:00pm. Compute the
probability that the number of hits to the Web site between 7:30pm and 7:35pm is:
a. Exactly seven
b. At least seven
37. The number of deaths in battles between Prussia and it’s enemies is given in the table.
a. What is the mean number of deaths?
b. What is the standard deviation?
c.
What is the probability that there were at least 2 deaths?
d. What is the probability that there were deaths?
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