MATH 6350

1
MATH 6350

• Ginger Holmes Rowell, Ph. D.

2
Homework Review

• Z-scores The Empirical Rule
• Chapter 1
• Examples
• Chapter 2
• What did you list?
• Chapter 3
• Bias Variability

3
Terms

• Population Parameter
• Sample Statistic

4
Chapter 1

• Student Examples

5
Chapter 2

• Students Points of Interest

6
Chapter 3

• Bias

• Variability

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Margin of Error
Chapter 3
/- 3

• Margin of error translates sampling variability
  into statements of how much confidence we can
  have in the results of a survey

For a different wording of this statement, see
the next slide.
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Margin of Error
Chapter 3
/- 3

• 3 Margin of Error means
• with repeated sampling, 95 of the samples
  gives a result that is within ( or -) 3 of the
  true value for the population

The only problem is that we usually do NOT know
the true value for the populations. Therefore
you do not know if your one sample provided a
result that was one of the 95 that was right or
one of the 5answers that is wrong.
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Margin of Error - Example
Chapter 3

• 56 of the MTSU students surveyed have a
  computer. (The survey has a ME of /- 5)
• Translate that sentence into one about the
  population of MTSU students. ____________________
  _____

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Margin of Error Sample Size
Chapter 3

• When estimating a population proportion from a
  sample proportion, then
• So, for a ME of 3, how many people do you need
  to survey?

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Confidence Statement
Chapter 3

• Confidence Statements
• Margin of Error how close the sample statistic
  lies to the population parameter
• Level of Confidence tells percent of all
  possible samples that satisfy the margin of error
  

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Confidence Statements (CS)
Chapter 3

• The conclusion of a CS ALWAYS applies to the
  population not the sample.
• Our conclusion about the population is NEVER
  completely certain.
• To get a smaller ME with the same level of
  confidence, take a larger sample.

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Population Size
Chapter 3

• Size of the population has little influence on
  the behavior of statistics from a random sample.
  
• As long as the sample is random the variability
  depends on the size of the sample.

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Increasing Sample Size
Chapter 3

• Increasing sample size
• Reduces variability if the sample is random
• Will NOT overcome bias if you use
• Convenience sampling
• Or voluntary response sampling

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Classwork
Chapter 3

• Text Page 42 5

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Homework
Chapter 3

• Chapter 3
• Finish Carefully Reading the Chapter
• Chapter Problems (p. 42)
• 1, 7, 8, 9, 11, 13, 21, 25, 27

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Sample Surveys
Chapter 4

• Errors in Sampling
• Sample Errors
• Random Sampling Errors
• Using Bad Sampling Methods
• Undercoverage

Q How does ME in a CS relate to sample error?
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Sample Surveys
Chapter 4

• Errors in Sampling
• Nonsampling Errors
• Processing Errors
• Response Errors
• Nonresponse Errors
• Even some question wordings can create bias

Q What does the ME in a CS NOT tell you?
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Sample Surveys
Chapter 4

• Dealing with nonsampling errors
• Nonresponse substitute other households for
  those that dont response
• Could be tricky
• Weight responses to correct for bias
• Adjust for factors differing from the population
  of interest

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Sample Surveys
Chapter 4

• More complicated sampling methods than the SRS
• Stratified Sample
• Definition _______________________
• Procedure ______________________
• Read Ex. 7 8, pg 58-59.
• Describe a mixed sampling method for telephone
  surveys (Hint Ex 9, p 60)

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Sample Surveys
Chapter 4

• Probability Sample
• Definition __________________
• Example
• ________________________

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Homework
Chapter 4

• Study page 61 for questions to ask before you
  believe a poll and then answer Q13, p.65
• End of the Chapter Questions
• Page 63
• 1, 3, 7, 9, 18, 21

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Hand-in Homework
Chapter 4

• Draft a survey that helps you find out the types
  of math and/or statistics examples that interest
  students.
• Maximum length 1 page
• Make it as simple as possible while still giving
  you the desired results.
• Email to me prior to 3pm on Wed. Sept. 10.
• Read Chapter 7 (p. 109 119)

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Experiments
Chapter 5

• Terms to Know
• Subjects
• Response Variable
• Explanatory Variable
• Treatment Variable

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Experiments
Chapter 5

• Terms you wish you did not need to know
• Lurking Variable
• Confounding Variables

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Experiments
Chapter 5

• Randomized Comparative Experiment

Randomize (Results in groups of subjects that
are similar in all respects Before treatment is
applied.)
Apply Treatment (Other influences operate
equally on all groups)
Result (If there is a difference, it is due to
the treatment.)
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Experiments
Chapter 5

• Words to the Wise
• Control
• Randomize
• Have a large enough sample size
• Term to Know
• Statistically Significant

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Experiments
Chapter 5

• Sometimes we can only Observe
• Observational Studies vs. Experiments
• Explain the differences ( p. 79-81)

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Real-World Experiments
Chapter 6

• Term
• Placebo
• Placebo Effect
• Double Blind Experiments
• Issues
• Refusals, Nonadherers, Dropouts
• What generalizations can be made?

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Real-World Experiments
Chapter 6

• Completely Randomized Design
• Matched Pairs Design
• Block Design (Randomized Block Design)

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Homework
Chapter 6

• Read Chapter
• Chapter 6, end of the chapter problems
• Page 102
• 3, 7, 9, 11, 17, 19

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Homework Review

• Ch 3 Read. Work problems
• Ch 4
• Read. Page 61, Problems.
• Hand-in design survey
• Ch 7 Read chapter
• Ch 5 Read chapter carefully
• Ch 6 Read. Work problems.