Transcript Chapter 01 Notes - Arizona State University

Chapter 1:
The Nature of Statistics
STP 226: Elements of Statistics
Jenifer Boshes
Arizona State University
1.1: Statistics Basics
Descriptive Statistics
Descriptive statistics consists of methods
for organizing and summarizing information.
Example 1:
(a) 80% of a class receives a passing grade.
(b) The Chicago Cubs had a winning record
of 97-64 for the 2008 season.
(c) The U.S. won 11.92% of the Gold Medals
in the 2008 Olympics.
Population & Sample
A population is the collection of all
individuals or items under consideration in
a statistical study.
A sample is the part of the population
from which information is obtained.
Inferential Statistics
Inferential statistics consists of methods
for drawing and measuring the reliability of
conclusions about a population based on
information obtained from a sample of the
population.
Example 2:
(a) Political polling.
(b) Archaeological digs.
(c) Average salary of a football player.
Descriptive vs. Inferential Statistics
(1) If the intent of the study is to examine
and explore the information obtained
for its own intrinsic interest only, the
study is descriptive.
(2) If the information is obtained from a
sample of a population and the intent
of the study is to use that information
to draw conclusions about the
population, the study is inferential.
Example 3a:
Classify the following studies as
descriptive or inferential.
(a) (Example 1.3; Page 6) The 1948
Presidential Election Ticket
Votes
Percentage
Truman-Barkley (Democratic)
24,179,345
49.7
Dewey-Warren (Republican)
21,991,291
45.2
Thurmond-Wright (States Rights)
1,176,125
2.4
Wallace-Taylor (Progressive)
1,157,326
2.4
139,572
0.3
Thomas-Smith (Socialist)
Example 3b:
Classify the following studies as
descriptive or inferential.
(b) (Example 1.4; Page 7) Testing Baseballs –
Major League Baseball used Spalding baseballs until 1976. In 1977, MLB
began using Rawlings baseballs (which are still in use today). In 1977,
pitchers complained that the baseballs were harder, bounced farther and
faster, and gave hitters an unfair advantage. An independent testing
company randomly selected a sample of 85 baseballs from the 1977
supplies of various major league clubs. The bounce, weight, and
hardness of the baseballs chosen was carefully measured and compared
with measurements obtained from similar tests on baseballs used in
1952, 1953, 1961, 1963, 1970, 1973. The conclusion was that “… the
1977 Rawlings ball is livelier than the 1976 Spalding, but not as lively as
it could be under big league rules, or as the ball has been in the past.”
Example 3c:
Classify the following studies as
descriptive or inferential.
Music Type
(c) (Problem 1.12; Page 10)
Music People Buy –
Results of monthly telephone surveys yielded
the percentage estimates of all music
expenditures shown in the table at the
top of the next column. These statistics
were published in 2001 Consumer
Profile.
Expenditure
(%)
Rock
24.4
Pop
12.1
Rap/Hip hop
11.4
R&B/Urban
10.6
Country
10.5
Religious
6.7
Jazz
3.4
Classical
3.2
Soundtracks
1.4
New Age
1
Oldies
0.8
Children's
0.5
Other
7.9
Unknown
6.1
Example 3d:
Classify the following studies as
descriptive or inferential.
(d) (Problem 1.11; Page 10)
Dow Jones Industrial
Averages The following table provides the closing
values of the Dow Jones Industrial
Averages as of the end of December for
the years 1997-2002.
Year
Closing
Value
1997
7,908.25
1998
9,181.43
1999
11,497.12
2000
10,786.85
2001
10,021.50
2002
8,341.63
1.2: Simple Random
Sampling
Acquiring Information
A census is obtaining information on the
entire population of interest.
Experimentation is conducting a
controlled study to come to conclusions
about a topic.
Sampling is a method of acquiring
information by choosing portions of a
population in a particular way to make
inferences.
Comments on Sampling
A representative sample reflects as
closely as possible the relevant
characteristics of the population under
consideration.
If you were interested in the average
height of an ASU student, who would
you include in your sample?
Probability Sampling
In probability sampling, a random
device, such as tossing a coin or
consulting a table of random numbers,
is used to decide which members of the
population will constitute the sample
instead of leaving such decisions to
human judgment.
The use of probability sampling
guarantees that the techniques of
inferential statistics can be applied.
Simple Random Sampling
Simple random sampling is a
sampling procedure for which each
possible sample of a given size is
equally likely to be the one obtained.
A simple random sample is a sample
obtained by simple random sampling.
(Unless otherwise specified, assume
simple random sampling is done without
replacement.)
Example 1:
The line of succession for the Presidency is:
Vice-President (V), Speaker of the House (H),
President pro tempore of the Senate (P), Secretary
of State (S), Secretary of the Treasury (T).
(a) List the 10 possible samples of size 2 that can be
obtained from the population of 5 officials.
(b) If a simple random sampling procedure is used to
obtain a sample of two officials, what are the
chances that it is the first sample on your list from
part (a)?
(c) What are some ways to obtain an SRS of size 2?
Table of Random Numbers
Appendix A
Table I
or Page 14
How to Use the
Random Number Table
Number the units of interest
Randomly select a starting point
Read down the column using the number
of digits of interest (i.e. If there are 50 units
of interest, use 2 digits. If there are 451
units of interest, use 3 digits.)
Record numbers, discarding repeats and
numbers outside the list of units.
Example 2:
Use the table of random numbers to
select eight years between 1950-1999
to study for your sample. Let the two
digit random number you select be the
year. For example, if you selected ‘62’,
study the year 1962. Begin with the
digits 79 in row/line 11, columns 07-08
of the random number table.
Example 3:
(Problem 1.28; Page 16) In the game of
keno, 20 balls are selected at random
from 80 balls, numbered 1-80. Use
Table I in Appendix A to simulate one
game of keno by obtaining 20 random
numbers between 1 and 80. Begin with
the digits 99 in row/line 07, columns 2223 of the random number table.
Bibliography
Some of the textbook images embedded in
the slides were taken from:
Elementary Statistics, Sixth Edition; by
Weiss; Addison Wesley Publishing
Company
Copyright © 2005, Pearson Education, Inc.