2. Statistical Reasoning p.295
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3. Fundamentals of Statistics
Unit 5A
Fundamentals of Statistics
The subject of statistics lays a major roll in modern society.
New drug effective in treating cancer
Involved when agricultural inspectors check the safety fo the food supply
Used in every opinion poll and survey
Used for market research in business
Sports stats are used in daily conversations for millions of people
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4. Two Definitions of Statistics
Statistics is the science of collecting, organizing, and interpreting data.
Statistics are the data that describe or summarize something.
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5. Definitions (example: American Idol)
The population in a statistical study is the complete set of people or things being studied.
The sample is the subset of the population from which the raw data are actually obtained.
Population parameters are specific characteristics of the population that a statistical study is designed to estimate.
Sample statistics are numbers or observations that summarize the raw data.
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6. Population and Sample CN (1a-d,2a-d)
For each of the following cases describe the a)population, b)sample, c)population parameters and d) sample statistics:
1. Agricultural inspectors for Jefferson County measure the levels of residue from three common pesticides on 25 ears of corn from each of the 104 corn-producing farms in the country.
2. Anthropologists determine the average brain size of early Neandertals in Europe by studying skulls found at three sites in southern Europe.
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7. Basic Steps in a Statistical Study
1. State the goal of your study precisely.
2. Choose a representative sample from the population.
3. Collect data from the sample and summarize these data by finding sample statistics of interest.
4. Use the sample statistics to infer the population parameters.
5. Draw conclusions.
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8. Elements of a Statistical Study
Help students understand this flow chart in the context of statistical research by perhaps using a contemporary example from a professional journal.
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9. Unemployment Survey CN (3a-e)
Each month, the US Labor Department surveys 60,000 households to determine characteristics of the US work force. One population parameter of interest is the US unemployment rate, defined as the percentage of people who are unemployed among all those who are either employed or actively seeking employment.
Describe how the five basic steps of a statistical study apply to this research. (List all five steps and give description of each)
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10. Definitions
A representative sample is a sample in which the relevant characteristics of the sample members match those of the population.
A statistical study suffers from bias if its design or conduct tends to favor certain results.
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11. Common Sampling Techniques
Stress that although a simple random sample may not be practical or necessary, it is still vital that the sample be as representative (unbiased) as possible in order to have valid data.
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12. Identify the Sampling Method Used
You are conducting a survey of students in a dormitory. You choose your sample by knocking on the door of every fifth room.
Choosing every fifth room makes this a systematic sample. The sample may be representative, as long as students were randomly assigned to rooms.
To survey opinions on a proposed new water line, a research firm randomly draws the addresses of homeowners from a public list of all homeowners.
The records presumably list all homeowners, so drawing randomly from this list produces a simple random sample. It has a good chance of being representative of the population.
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13. Sampling Methods CN (4-7)
Identify the type of sampling used in each of the following cases, and comment on whether the sample is likely to be representative of the population.
4. You are conducting a survey of student sin a dormitory. You choose your sample by knocking on the door of every 10th room.
5. To survey opinions on a possible property tax increase, a research firm randomly draws the addresses of 150 home owners from a public list of all homeowners.
6. Agricultural inspectors for Jefferson County check the levels of residue from three common pesticides on 25 ears of corn from each of the 104 corn-producing farms in the county.
7. Anthropologists determine the average brain size of early Neandertals in Europe by studying skulls found at three sites in southern Europe.
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14. Types of Statistical Study
In an observational study, researchers observe or measure characteristics of the sample members but do not attempt to influence or modify these characteristics.
In an experiment, researchers apply a treatment to some or all of the sample members and then look to see whether the treatment has any effects.
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15. Treatment and Control Groups
The treatment group in an experiment is the group of sample members who receive the treatment being tested.
The control group in an experiment is the group of sample members who do not receive the treatment being tested.
It is important for the treatment and control groups to be selected randomly and to be alike in all respects except for treatment.
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16. Placebos and the Placebo Effect
A placebo lacks the active ingredients of a treatment being tested in a study, but is identical in appearance to the treatment. Thus, study participants cannot distinguish the placebo from the real treatment.
The placebo effect refers to the situation in which patients improve simply because they believe they are receiving a useful treatment.
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17. Blinding in Experiments
An experiment is single-blind if the participants do not know whether they are members of the treatment group or members of the control group, but the experimenters do know.
An experiment is double-blind if neither the participants nor the experimenters (people administering the treatment) know who belongs to the treatment group and who belongs to the control group.
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18. What’s Wrong with this Experiment? CN (8-9)
For each of the experiments described below, identify any problems and explain how the problems could have been avoided.
8. A chiropractor wants to know if his adjustments relieve back pain. He performs adjustments on 25 patients with back pain. Afterward, 18 of the patients say they feel better. He concludes that the adjustments are an effective treatment.
9. A new drug for attention deficit disorder (ADD) is supposed to make the affected children more polite. Randomly selected children suffering from ADD are divided into treatment and control groups. Those in the control group receive a placebo that looks just like the real drug. The experiment is single-blind. Experimenters interview the children one-on-one to decide whether they became more polite.
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19. Definitions
A case-control study is an observational study that resembles an experiment because the sample naturally divides into two (or more) groups.
The participants who engage in the behavior under study form the cases.
The participants who do not engage in the behavior are the controls.
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20. Which type of Study? CN (10-13)
For each of the following questions, what type of statistical study is most likely to lead to an answer? Why?
10. What is the average income of stock brokers?
11. Do seat belts save lives?
12. Can lifting weights improve runners’ times in a 10-kilometer race?
13. Can a new herbal remedy reduce the severity of colds?
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21. Definitions
The margin of error is used to describe a confidence interval that is likely to contain the true population parameter.
A confidence interval is
from (sample statistic − margin of error)
to (sample statistic + margin of error).
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22. Close Election CN (14)
An election eve poll finds that 52% of surveyed voters plan to vote for Smith, and she needs a majority (more than 50%) to win without a runoff. The margin of error in the poll is 3 percentage points.
14. Will she win?
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23. Quick Quiz 1-10 CN (15)
Choose the best answer to each of the 10 questions on p.307.
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24. 5A Homework p.307: 1-14, 1 web, 1 world, CN 1-15
Review Questions 1-8
Does it make sense 9-14
1 web
61. Current Nielsen Ratings
62. Attitude Update
63. Labor Statistics
64. Professional Polling
1 world
65. Statistics in the News
66. Statistics in Your Major
67. Statistics in Sports
68. Poor Sampling
70. Good Sampling
71. Margin of Error
Class Notes 1-15