AP%20STATISTICS%20REVIEW%20INFERENCE

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AP STATISTICSREVIEWINFERENCE
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Statistical Inference

• Drawing conclusions (to infer) about a
  population based upon data from a sample.
• Two types of inference
• Confidence intervals
• Significance tests

USB Documents\AP STATISTICS\quick guide to
inference.pdf
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Confidence Intervals
Confidence intervals estimate the true value of
the parameter where the parameter is the true
mean , true proportion p, or true slope .
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Confidence Intervals

• 1-sample t-interval for
• 2-sample t-interval for
• Matched-pairs t-interval
• 1-proportion z-interval for p
• 2-proportion z-interval for p1 - p2
• t-interval for slope

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Confidence Intervals
P A C S
Parameters
Assumptions (conditions)
Calculate interval
State a conclusion
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Interpret the confidence level

• C of all intervals produced using this method
• will capture the true mean (difference in means),
  or proportion (difference in proportions), or
  slope.
• (Describe the parameter in context!)

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Interpret the confidence interval

• I am C confident that the true parameter (insert
  context) is between ___ and ___ (insert units),
  based on this sample.

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(2000) Question 6

• A random sample of 400 married couples was
  selected from a large population of married
  couples.
• Heights of married men are approximately normally
  distributed with a mean 70 inches and standard
  deviation 3 inches.
• Heights of married women are approximately
  normally distributed with mean 65 inches and
  standard deviation 2.5 inches.
• There were 20 couples in which the wife was
  taller than her husband, and there were 380
  couples in which the wife was shorter than her
  husband.
• Find a 95 percent confidence interval for the
  proportion of married
• couples in the population for which the wife is
  taller than her husband. Interpret your interval
  in the context of this question.

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Solution (2000 Question 6, part a)
Parameter, Assumptions, Test Name (or formula)
p true proportion of married couples in which
the wife is taller than her husband

• Assumption large sample size since

1-proportion z-interval for p
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Solution (2000 Question 6, part a)

• Calculations

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Solution (2000 Question 6, part a)

• Interpret the interval

I am 95 confident that the true proportion of
couples in which the wife is taller than her
husband is between .028 and .071, based on this
sample.
USB Documents\AP STATISTICS\AP Stats\correct
incorrect ways to explain CI.doc
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Significance Tests
H A T S
Hypothesis (define parameters!)
Assumptions (conditions)
Test name or formula
State a conclusion
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Significance Tests

• Significance tests provide evidence for some
  claim using sample data.
• test statistic

estimated value hypothesized value
standard error of the estimate
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Significance Tests

• 1-sample t-test for
• 2-sample t-test for
• Matched pairs t-test
• 1-proportion z-test for p
• 2-proportion z-test for p1 p2
• Chi-square goodness-of-fit test
• Chi-square test for homogeneity or
  independence/association
• t-test for slope ?

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What is the P-value?

• The P-value is the probability of getting an
  observation as extreme or even more extreme by
  chance alone, assuming that the null hypothesis
  is true.
• If the P-value is small (lt alpha), then we reject
  Ho and accept Ha. (Results are statistically
  significant)
• If the P-value is large (gt alpha), then we fail
  to reject Ho and fail to accept Ha. (Results are
  not statistically significant)

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Know your inference procedures

• Helpful web site http//www.ltcconline.net/greenl
  /java/Statistics/StatsMatch/StatsMatch.htm

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(2000) Question 4
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Solution (2000) Question 4
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Solution (2000) Question 4
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Solution (2000) Question 4
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Solution (2000) Question 4
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Solution (2000) Question 4
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Solution (2000) Question 4
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Scoring (2000) Question 4
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Scoring (2000) Question 4
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(2003) Question 5
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Solution (2003) Question 5
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Solution (2003) Question 5
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Solution (2003) Question 5
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Solution (2003) Question 5
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Scoring (2003) Question 5
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Type I, Type II Errors Power

• Type I Error (?)
• Ho is true, but we reject Ho ( support Ha)
• Type II Error (??)
• Ho is false, but we fail to reject Ho ( fail
  to
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  support Ha)
• Power (1- ?)
• the probability of correctly rejecting Ho

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Type I, Type II Errors Power
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How to increase power

• Increase alpha (level of significance)
• Increase the sample size, n
• Decrease variability
• Increase the magnitude of the effect (the
  difference in the hypothesized value of a
  parameter its true value

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(2003) Question 2
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Solution (2003) Question 2
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Solution (2003) Question 2
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Solution (2003) Question 2
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Scoring (2003) Question 2
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Scoring (2003) Question 2
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Scoring (2003) Question 2
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Scoring (2003) Question 2
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• Good Luck!