Chapter 1: Getting Started Section:1'1 What is statistics

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Chapter 1 Getting Started Section1.1 What is
statistics?

• Statistics is the study of how to collect ,
  organize , analyze, and interpret numerical
  information from data.
• Individual is people or object included in a
  study.
• Variable is a characteristic of the individual to
  be measured or observed.

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Section1.1 What is statistics?

• Quantitative Variable has a value or numerical
  measurement.
• ----example height of a person.
• Qualitative Variable (categorical) places an
  individual in a category or group.
• -----example gender of a person.

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Section1.1 What is statistics?

• Population data Variable is from every
  individual of interest.
• -----example Income of all the residents of a
  county.
• Sample data Variable is from only some of the
  individual of interest.
• -----example Income of selected residents.

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Section1.1 What is statistics?

• Example 1 Television station QUE wants to know
  the proportion of TV owners in Virginia who watch
  the stations new program at least one a week.
  The station asked a group of 1000 TV owners in
  Virginia if they watch the program at least once
  a week.
• Identify the individuals of the study and the
  variable?
• Do the data comprise a sample? If so, what is the
  underlying population?
• Is the variable quantitative or qualitative?
• Identify a quantitative variable that might be of
  interest?

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Section1.1 What is statistics?

• Level of Measurement

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Section1.1 What is statistics?

• Branches of Statistics
• Descriptive methods of organizing, picturing,
  and summarizing information.
• Inferential methods of using information from a
  sample to draw conclusions regarding the
  population.

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Section1.2 Random Samples?

• Methods of Producing Data
• Sampling drawing subsets from the population
• Experimentation impose a change and measure the
  result
• Simulation arithmetic imitation of real
  phenomena
• Census using measurements from entire population
• Survey asking questions

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Section1.2 Random Samples?

• Simple Random Sample of n measurements
• (a) every sample of size n from the
  population has an equal chance of being selected
  and
• (b) every member of the population has an
  equal chance of being included in the sample.

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Section1.2 Random Samples?

• Example 1 Suppose you pay one dollar and choose
  any six different numbers from the group of
  numbers 1 through 42. If your group of six
  numbers matches the winning group of six numbers
  selected by simple random sampling, then you are
  a winner of a grad prize of at least 1.5 million
  dollars.
• Is the number 25 as likely to be selected in the
  winning group of six numbers as the number 5?
• Could all the wining numbers be even?
• Your friend always plays the numbers
• 1 2 3 4 5 6
• Could she ever win?

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Section1.2 Random Samples?

• Not Random Sampling
• Examples (a) Ask for volunteers to
  respond to a survey
• (b) choosing the first
  five customers in a store.
• How do you get random Samples?
• drawing names from from a hat
• using a random number table to select sample
• using a random number generator

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Section1.2 Random Samples?

• Example 2 Use a random table to pick a
  (simple )random sample of 30 cars from a
  population of 500 cars.
• Solution We assign each car a different number
  between 1 and 500, inclusive. Then we use the
  random number table (Table 1 in Appendix II) to
  choose the sample. Table 1 in Appendix II has 50
  rows and 10 blocks of five digits each it can be
  thought of as a solid mass of digits that has
  been broken up into rows and blocks for user
  convenience.
• You read the digits by beginning
  anywhere in the table. We dropped a pin on the
  table, and the head of the pin landed in raw 18,
  block 3. We will begin there and list all the
  digits in that row. If we need more digits, we
  will move on to the raw 19. The digits we begin
  with are
• 67967 07835 11314 01545 48535
  17142 etc
• Since the highest number assigned to a car is
  500, this number has three digits, we regroup the
  digits into blocks of three
• 679 670 783 511 314
  015 454 853 517 142
  etc

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Section1.2 Random Samples?

• Note Another important use random number tables
  is in simulation.
• Examples 3 Use a random-number table to
  simulate the outcomes of tossing a balanced (that
  is, fair) penny 10 times.
• (a) How many outcomes are possible when you
  toss a coin once? Two heads or tails
• (b) There are several ways to assign a fair
  coin, assign an even digit to the outcome heads
  and an odd digit to the outcome tails. 7 1
  5 4 9 4 4 8 4 3
• (c) What are the outcomes associated with 10
  digits? T T T H T H H H H T
• (d) If you start in a different block and
  row of Table 1 in Appendix II, will you get the
  same sequence of outcomes. It is possible, but
  not very likely.

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Section1.2 Random Samples?

• Note Sampling with replacement means
  that although a number is selected for the
  sample, it is not removed from the population.
  Therefore, the same number may be selected for
  the sample more than once. If you need to sample
  without replacement, generate more items than you
  need for the sample. Then sort the sample and
  remove duplicate values.

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Section1.2 Random Samples?

• Other Sampling Techniques
• Stratified sampling
• Systematic sampling
• Cluster sampling
• Convenience sampling

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Section1.3 Introduction to Experimental Design

• Planning a Statistical Study and gathering
  data are essential components for obtaining
  reliable information.

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Section1.3 Introduction to Experimental Design

• Basic Guidelines for planning a statistical
  study
• First, identify the individuals or objects of
  interest.
• Specify the variables as well as the protocols
  for taking measurements or making observations.
• Determine if you will use an entire population
  or a representative sample. If using a sample,
  decide on a viable sampling method.
• In your data collection plane, address the issues
  of ethics, subject confidentiality, and privacy.
  If you are collecting data at a business, store,
  college, or other institution, be sure to be
  courteous and to obtain permission as necessary.
• Collect the data
• Use appropriate descriptive statistics methods
  and make decisions using appropriate statistical
  methods.
• Finally, note any concerns you might have your
  data collection methods and list any
  recommendations for the future studies.

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Section1.3 Introduction to Experimental Design

• Types of Studies
• When gathering data for statistical
  study, we want to distinguish between
  observational studies and experiments.
• In an observational study, observations
  and measurements of individuals are conducted in
  a way that doesnt change the response or the
  variable being measured.
• In an experiment, a treatment is
  deliberately imposed on the individuals in order
  to observe a possible change in the response or
  variable being measured.

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Section1.3 Introduction to Experimental Design

• Statistical experiments are commonly used to
  determine the effect of a treatment. However, the
  design of the experiment needs to control for
  other possible causes of the effect. For
  instance, in medical experiments the placebo
  effect is the improvement or change that is the
  result of patients just believing in the
  treatment, whether or not the treatment itself is
  effective,

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Section1.3 Introduction to Experimental Design

• The placebo effect occurs when a subject
  receives no treatment, but (incorrectly) believes
  he or she is in fact receiving treatment and
  responds favorably.
• To account for the placebo effect,
  patients are divided into two groups. One group,
  is called treatment group, receives the
  prescribed treatment. The other group, called
  the control group, receives a dummy or placebo
  treatment that is disguised to look the real
  treatment.

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Section1.3 Introduction to Experimental Design

• In general, a control group is used to
  account for the influence of other known or
  unknown variables that might be an underlying
  cause of a change in response in the treatment
  or experimental group. Such variables are called
  lurking or confounding variable.
• A common way to assign patients to the
  treatment and control groups is by using a random
  process. This is the essence of a randomized
  two-treatment experiment.
• Many experiments are also double-blind.
  This means that neither the individuals in the
  study nor the observers know which subjects are
  receiving the treatment. Double-blind experiment
  help control for subtle biases that a doctor
  might pass to a patient.

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Chapter 1 Homework/Class Exercises

• Homework/Class Exercises
• Section 1.1 1, 3, 7, 9 (page 11-13)
• Section 1.2 3, 5, 6, 8, 14 (page 19-21)
• Section 1.3 1, 3, 5 (page 29-31)

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Chapter 2 Homework/Class Exercises

• Homework/Class Exercises
• Section 2.1 1, 3, 7, 9, 11 (page 49-51)
• Section 2.2 1, 5, 7, 11 (page 67-70)
• Section 2.3 2, 3 (page 80)

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Chapter 3 Homework/Class Exercises

• Homework/Class Exercises
• Section 3.1 1, 2, 11 (a and b), 17, 21 (page
  106-110)
• Section 3.2 1, 2, 5, 7, 9, 15 (page 121-124)
• Section 3.3 3, 5 (page 131)
• Section 3.4 5, 7 (page 143)

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Chapter 4 Homework/Class Exercises

• Homework/Class Exercises
• Section 4.1 1, 3, 4, 5, 8, 9, 10, 13 (page
  171-173)
• Section 4.2 1, 3, 4, 5, 7, 9, 11, 15, 13, 17,
  19 (page 188-192)

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Chapter 5 Homework/Class Exercises

• Homework/Class Exercises
• Section 5.1 3, 5, 7, 9, 13, 15 (page 227-231)
• Section 5.2 1, 3, 5, 8, 11 (page 188-192)
• Section 5.3 5 (page 257)

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Chapter 6 Homework/Class Exercises

• Homework/Class Exercises
• Section 6.1 5, 7, 9, 13 (page 304-306)
• Section 6.2 1, 3, 5, 7(page 319-321)
• Section 6.3 3, 5, 7, 9, 11, 13, 15, 17, 21, 23,
  24 (page 330-331)
• Section 6.4 1, 3 (page 341)

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Chapter 7 Homework/Class Exercises

• Homework/Class Exercises
• Section 7.11, 2, 3, 4, 6 (page 365)
• Section 7.2 1, 3, 7, 10(page 373-375)
• Section 7.3 2, 3, 4, 5, 7, 8, 9 (page 387-389)

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Chapter 8 Homework/Class Exercises

• Homework/Class Exercises
• Section 8.11, 3, 4, 7, 9 (a and b )(page
  410-411)
• Section 8.2 1, 2, 5, 6, 7, 8, 16, 17(page
  420-424)
• Section 8.3 1, 2, 3, 7, 8, 16, 17(page 433-434)
• Section 8.4 1, 5, 9(page 441-443)
• Section 8.5 1, 5, 8, 15(page 459-463)

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Chapter 9 Homework/Class Exercises

• Homework/Class Exercises
• Section 9.1 3, 5, 6, 9, 10, 11, 13 (page
  494-497)
• Section 9.2 1, 3, 5, 6, 9, 10, 13, 15(page
  510-513)
• Section 9.3 1, 3, 5, 7 (page 522-523)
• Section 9.4 1, 3, 6,13, 15 (page 535-541)
• Section 9.5 1, 5, 7, 9, 11, 17, 19, 21, 24 (page
  558-564)

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Chapter 10 Homework/Class Exercises

• Homework/Class Exercises
• Section 10.1 1, 2, 7, 8, 9, 10, 11 (page
  595-597)
• Section 10.2. 1, 3, 5 (page 614-615)

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Chapter 11 Homework/Class Exercises

• Homework/Class Exercises
• Section 11.1 1, 2, 3, 5 (page 681-683)
• Section 11.2. 1, 3, 4, 5, 7, 8 (page 691-693)