Download Statistics -- Exam I Review Note: This is only a sample of exercises

Statistics -- Exam I Review
Note: This is only a sample of exercises. Anything covered in class may appear on the exam.
Determine whether the given value is a statistic or a parameter.
1) A sample of 120 employees of a company is selected, and the average age is found to be 37 years.
2) After inspecting all of 55,000 kg of meat stored at the Wurst Sausage Company, it was found that 45,000 kg of
the meat was spoiled.
Identify the number as either continuous or discrete.
3) The number of freshmen entering college in a certain year is 621.
4) The number of limbs on a 2-year-old oak tree is 21.
5) The height of 2-year-old maple tree is 28.3 ft.
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.
6) The sample of spheres categorized from softest to hardest.
7) Nationalities of survey respondents.
8) Amount of fat (in grams) in cookies.
9) The temperatures of eight different plastic spheres.
Identify the sample and population. Also, determine whether the sample is likely to be representative of the population.
10) An employee at the local ice cream parlor asks three customers if they like chocolate ice cream.
11) 100,000 randomly selected adults were asked whether they drink at least 48 oz of water each day and only 45%
said yes.
Perform the requested conversions. Round decimals to the nearest thousandth and percents to the nearest tenth of a
percent, if necessary.
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12) Convert the fraction to an equivalent decimal and percentage.
4
13) Convert 0.4 to an equivalent fraction and percentage.
14) Convert 49% to an equivalent fraction and decimal.
Solve the problem.
15) Alex and Juana went on a 50-mile canoe trip with their class. On the first day they traveled 29 miles. What
percent of the total distance did they canoe?
Is the study experimental or observational?
16) A marketing firm does a survey to find out how many people use a product. Of the one hundred people
contacted, fifteen said they use the product.
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17) A quality control specialist compares the output from a machine with a new lubricant to the output of machines
with the old lubricant.
Identify the type of observational study.
18) A statistical analyst obtains data about ankle injuries by examining a hospital's records from the past 3 years.
A) Prospective
B) Cross-sectional
C) Retrospective
D) None of these
19) A researcher plans to obtain data by following those in cancer remission since January of 2002.
A) Cross-sectional
B) Retrospective
C) Prospective
D) None of these
20) A town obtains current employment data by polling 10,000 of its citizens this month.
A) Retrospective
B) Cross-sectional
C) Prospective
D) None of these
Identify which of these types of sampling is used: random, stratified, systematic, cluster, convenience.
21) 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481
students respectively.
22) To avoid working late, a quality control analyst simply inspects the first 100 items produced in a day.
23) A market researcher selects 500 people from each of 10 cities.
24) A sample consists of every 49th student from a group of 496 students.
Solve the problem.
25) The following frequency distribution analyzes the scores on a math test. Find the indicated class midpoint or
boundaries.
The class boundaries of scores interval 40-59
26) The following frequency distribution analyzes the scores on a math test. Find the indicated class midpoint or
boundaries.
The class midpoint of scores interval 40-59
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27) Using the information in the table on home sale prices in the city of Summerhill for the month of June, find the
class midpoint for class 235.0-265.9.
Class Limits
Frequency
(Sale price in thousands) (No. of homes sold)
80.0 - 110.9
2
111.0 - 141.9
5
142.0 - 172.9
7
173.0 - 203.9
10
204.0 - 234.9
3
235.0 - 265.9
1
Use the given data to construct a frequency distribution.
28) Kevin asked some of his friends how many hours they had worked during the previous week at their
after-school jobs. The results are shown below.
6 6 6 3 6 6 9 8 6 3 8 6
6 8 6 6 8 6 6 8 6 8 8 3
Construct a frequency table. Use 4 classes, a class width of 2 hours, and a lower limit of 3 for class 1.
Hours Frequency
29) Lori asked 24 students how many hours they had spent doing homework during the previous week. The results
are shown below.
10 10 10 9 10 10 14 13 10 9 12 10
10 12 10 10 12 10 10 13 10 12 13 9
Construct a frequency table. Use 4 classes, a class width of 2 hours, and a lower limit of 8 for class 1.
Hours
Frequency
3
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. Use the histogram to answer the
question. The blood pressure readings were given to the nearest whole number.
30) Approximately what percentage of the people aged 25-40 had a systolic blood pressure reading between 110
and 119 inclusive?
Solve the problem.
31) In a survey, 26 voters were asked their ages. The results are shown below. Construct a histogram to represent the
data (with 5 classes beginning with a lower class limit of 19.5 and a class width of 10). What is the approximate
age at the center?
43 56 28 63 67 66 52 48 37 51 40 60 62
66 45 21 35 49 32 53 61 53 69 31 48 59
4
Use the circle graph to solve the problem.
32) A survey of the 5589 vehicles on the campus of State University yielded the following pie chart.
9%
16%
36%
8%
6%
25%
What percent of the vehicles are hatchbacks?
Find the original data from the stem-and-leaf plot.
33)
Stem Leaves
3
59
4
19
5
55
Construct the dot plot for the given data.
34) 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
Use the data to create a stemplot.
35) The midterm test scores for the seventh-period typing class are listed below.
85 77 93 91 74 65 68 97 88 59 74 83 85 72 63 79
Find the mean for the given sample data.
36) Six college buddies bought each other Christmas gifts. They spent:
$122.34 $233.13 $222.32
$130.44 $165.25 $197.41
What was the mean amount spent? Round your answer to the nearest cent.
37) Bill kept track of the number of hours he spent exercising each week. The results for four months are shown
below. Find the mean number of hours Bill spent exercising per week. Round your answer to two decimal
places.
6.90 6.60 6.70 6.90 7.20 6.90
7.40 6.70 8.10 6.90 6.90 6.70
8.80 6.60 6.60 7.70 7.20 7.40
5
Find the median for the given sample data.
38) The number of vehicles passing through a bank drive-up line during each 15-minute period was recorded. The
results are shown below. Find the median number of vehicles going through the line in a fifteen-minute period.
30 32 30 33
33 30 35 32
40 36 36 34
29 36 30 25
20 32 32 32
Find the mode(s) for the given sample data.
39) The weights (in ounces) of 14 different apples are shown below.
5.5 4.2 6.9 4.6 4.5 5.5 4.2
5.0 6.2 4.6 5.5 5.0 4.6 4.7
Find the midrange for the given sample data.
40) 3 6 9 0 4 1 11 5
9 14 3 8 2 15 0 9
Find the mean of the data summarized in the given frequency distribution.
41) A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the
mean salary.
Salary ($) Employees
5,001-10,000
16
10,001-15,000
14
15,001-20,000
15
20,001-25,000
17
25,001-30,000
18
Find the range for the given data.
42) The owner of a small manufacturing plant employs six people. As part of their personnel file, she asked each
one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The six
distances are listed below:
2.6 5.4 1.6 4.9 6.7 3.8
Compute the range.
Find the variance for the given data. Round your answer to one more decimal place than the original data.
43) 3.8, 1.9, 8.8, 3.3, and 4.2
Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results.
44) When investigating times required for drive-through service, the following results (in seconds) were obtained.
Restaurant A 120 123 153 128 124 118 154 110
Restaurant B 115 126 147 156 118 110 145 137
Solve the problem.
45) The heights in feet of people who work in an office are as follows. Use the range rule of thumb to find the
standard deviation. Round results to the nearest tenth.
5.9 6.0 5.8 5.4 6.0 5.5 6.0 6.2 6.1 5.5
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Solve the problem. Round results to the nearest hundredth.
46) Scores on a test have a mean of 71 and a standard deviation of 9. Michelle has a score of 89. Convert Michelle's
score to a z-score.
47) The mean height of a basketball team is 6.1 feet with a standard deviation of 0.2 feet. The team's center is 6.7 feet
tall. Find the center's z score. Is his score unusual?
Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual.
Consider a score to be unusual if its z-score is less than -2.00 or greater than 2.00. Round the z-score to the nearest tenth
if necessary.
48) A test score of 54.0 on a test having a mean of 73 and a standard deviation of 10.
49) A weight of 220 pounds among a population having a mean weight of 161 pounds and a standard deviation of
23.5 pounds.
Determine which score corresponds to the higher relative position.
50) Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a
test with a mean of 493 and a standard deviation of 150?
Find the percentile for the data point.
51) Data set: 55 46 30 63 63 65 42;
data point 55
Find the indicated measure.
52) Use the given sample data to find Q3 .
49 52 52 52 74 67 55 55
53) The weights (in pounds) of 30 newborn babies are listed below. Find P16.
5.5 5.7 5.8 5.9 6.1 6.1 6.4 6.4 6.5 6.6
6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.2
7.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7
Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots.
54) The weights (in pounds) of 30 newborn babies are listed below. Construct a boxplot for the data set.
5.5 5.7 5.8 5.9 6.1 6.1 6.3 6.4 6.5 6.6
6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.2
7.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7
55) The test scores of 32 students are listed below. Construct a boxplot for the data set.
32 37 41 44 46 48 53 55
57 57 59 63 65 66 68 69
70 71 74 74 75 77 78 79
81 82 83 86 89 92 95 99
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Answer Key
Testname: EXAM I REVIEW
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
Statistic
Parameter
Discrete
Discrete
Continuous
Ordinal
Nominal
Ratio
Interval
Sample: the 3 selected customers; population: all customers; not representative
Sample: the 100,000 selected adults; population: all adults; representative
0.75, 75%
2
13) , 40%
5
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
49
, 0.49
100
58%
Observational
Experimental
C
C
B
Stratified
Convenience
Cluster
Systematic
39.5, 59.5
49.5
250.45
Hours Frequency
3-4
3
5-6
13
7-8
7
9 - 10
1
Hours Frequency
8-9
3
10 - 11
13
12 - 13
7
14 - 15
1
30) 35%
8
Answer Key
Testname: EXAM I REVIEW
31) The approximate age at the center is 50.
32) 36%
33) 35, 39, 41, 49, 55, 55
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
51)
52)
53)
54)
5 9
6 358
7 24479
8 3558
9 137
$178.48
7.12
32
5.5, 4.6
7.5
$17,937.50
5.1
6.81
Restaurant A: 44; 260.79; 16.15
Restaurant B: 46; 285.64; 16.90
0.2
2
3, yes
-1.9; not unusual
2.5; unusual
A score of 92
43
61.0
6.1
9
Answer Key
Testname: EXAM I REVIEW
55)
10