STAT2910_Chap1&2_Tutorial_W24
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School
University of Windsor *
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Course
2910
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
4
Uploaded by LieutenantWaspMaster985
Department of Mathematics and Statistics
STAT2910-01: Statistics for Sciences
Faculty of Science
University of Windsor
Tutorial for Chapter 1 and 2
Questions for Chapter 1
Exercise 1.
Identify each of the following variables as either quantitative or qualitative
a.
the brands of ice cream that you purchase
b.
the daily high temperature for the past four weeks
c.
the amount of sugar consumed by Canadians in one year
d.
the species of fish in the zoo
e.
the lengths of time children wait for the school bus
f.
your favourite professional football team
Exercise 2.
Identify each of the following variables as qualitative or quantitative.
a.
rating of the effectiveness of a new cold remedy (not effective, effective)
b.
amount of time spent assembling a five-shelf bookcase
c.
number of children in a beginners’ swimming class
d.
university where a student is enrolled
e.
color preference for a nursery
f.
rating the Canadian foreign policy in the Middle East (fair, biased)
Exercise 3.
Identify each of the following quantitative variables as discrete or continuous.
a.
average monthly temperature for a particular city
b.
number of employees of a statistical consulting firm who own laptop computers
c.
flight time between two cities
d.
number of puppies enrolled in an obedience class
e.
number of persons on a flight from Chicago to Calgary
f.
amount of gas purchased at a gas station
1
Exercise 4.
Classify the following variables, first as qualitative or quantitative and second, if quantitative, as discrete
or continuous:
a.
the colors of cars at an auction
b.
the amount of money spent on building a new school
c.
the genders of members of parliament
d.
the styles of houses (1-story, 2-story, split level, etc.)
e.
the letter grades of students in a statistics exam (A, B, C, D, F)
f.
the number of credit cards owned by customers
Exercise 5.
The length of time (in months) between the onset of a particular disease and its recurrence was recorded
for
n
= 48:
0.1
2.1
4.4
1.6
2.7
9.9
9.0
2.0
6.6
3.9
14.7
9.6
16.7
7.4
8.2
19.2
6.9
4.3
3.3
1.2
4.1
18.4
0.2
6.1
13.5
7.4
0.2
8.3
0.3
1.3
14.1
1.0
2.4
2.4
18.0
8.7
24.0
1.4
8.2
5.8
1.6
3.5
11.4
3.7
12.6
23.1
5.6
0.4
a.
Construct a relative frequency histogram for the data (use class width = 8).
b.
Would you describe the shape as roughly symmetric, skewed to the right, or skewed to the left?
c.
Give the fraction of recurrence times less than 15.1 months.
d.
Construct a steam-and-leaf plot with unit 0.1.
Exercise 6.
Construct a stem-and-leaf plot for the following set of data.
28
13
26
12
20
14
21
16
17
22
17
25
13
30
13
22
15
21
18
18
16
21
18
31
15
19
Exercise 7.
The calcium (Ca) content of a powdered mineral substance was analyzed ten times with the following
percent compositions recorded:
0
.
0271
,
0
.
0282
,
0
.
0279
,
0
.
0281
,
0
.
0268
,
0
.
0271
,
0
.
0281
,
0
.
0269
,
0
.
0275
,
0
.
0276
.
a.
Draw a stem and leaf plot for the data. Use the numbers in the hundredths and thousandths places
as the stem.
b.
Are any of the measurements inconsistent with the other measurements, indicating that the technician
may have made an error in the analysis?
2
Questions for Chapter 2
Exercise 8.
The following data represent the number of small cracks per bar for a sample of eight steel bars: 4, 6, 10,
1, 3, 1, 25, and 8.
a.
What is the average number of small cracks per bar?
b.
Find the standard deviation for the number of small cracks per bar.
c.
Which, if any, of the observations appear to be outliers? Justify your answer.
Exercise 9.
Twenty-eight applicants interested in working in community services took an examination designed to
measure their aptitude for social work. A stem-and-leaf plot of the 28 scores appears below, in which the
first column is the count per “branch,” the second column is the stem value, and the remaining digits are
the leaves.
4
6
5
9
6
3688
7
026799
8
145667788
9
1234788
a.
What is the range of these data?
b.
What is the median score?
c.
What is the sample mean for this data set?
d.
What is the value of the sample standard deviation?
e.
Should the Empirical Rule be applied to this data set?
f.
Use the range approximation to determine an approximate value for the standard deviation. Is this a
good approximation?
g.
What is the value of the first and third quartiles?
h.
What is the interquartile range?
Exercise 10.
A new manufacturing plant has 20 job openings. To select the best 20 applicants from among the 1000
job seekers, the plant’s personnel office administers a written aptitude test to all applicants. The average
score on the aptitude test is 150 points, with a standard deviation of 10 points. Assume the distribution
of test scores is approximately mound-shaped.
a.
What percentage of the test scores will fall between 130 and 160 points?
b.
How many applicants will score between 130 and 160 points?
c.
One of the applicants scored 192 points on the test. What might you conclude about this test score?
3
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Exercise 11.
Consider the following set of measurements:
5
.
4
,
5
.
9
,
3
.
5
,
4
.
1
,
4
.
6
,
2
.
5
,
4
.
7
,
6
.
0
,
5
.
4
,
4
.
6
,
4
.
9
,
4
.
6
,
4
.
1
,
3
.
4
,
2
.
2
.
a.
Find the mean, median, variance and standard deviation of this sample
b.
Find the 25th, 50th, and 75th percentiles
c.
What is the value of the interquartile range?
Exercise 12.
The following data represent the scores for a sample of 10 students on a 20-point chemistry quiz: 16, 14,
2, 8, 12, 12, 9, 10, 15, and 13. Calculate the z-score for the smallest and largest observations. Is either of
these observations unusually large or unusually small?
Exercise 13.
Two students are enrolled in different sections of an introductory statistics class at a local university. The
first student, enrolled in the morning section, earns a score of 76 on a midterm exam where the class
mean was 64 with a standard deviation of 8. The second student, enrolled in the afternoon section, earns
a score of 72 on a midterm exam where the class mean was 60 with a standard deviation of 7.5. If the
scores on the midterm exams are normally distributed, which student scored better relative to his or her
classmates?
Exercise 14.
a.
If the 90th and 91st observations in a set of 100 data values are 158 and 167, respectively, what is the
90th percentile value?
b.
If the 18th and 19th observations in a set of 25 data values are 42.6 and 43.8, what is the 70th percentile
value?
4