Making Inferences for Single Variables Chapter 11

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Making Inferences for Single VariablesChapter 11

• Reading Assignment
• pp. 432-453

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Terminology

• Point Estimate a characteristic of a sample
  being used to estimate a population parameter
• Recall population parameter is a statistical
  characteristic such as mean, median, mode or a
  percentage
• Confidence Interval a range of values within a
  given point estimate is likely to fall the
  confidence level specifies how likely it is that
  a point estimate will fall in a given range

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Terminology 3

• Recall
• Std dev of sampling distribution of sample
  meansalso called the standard error of the mean
• Formula 10.5
• Follow ex for std error age
• Skills 1, p. 435
• Follow SPSS guide

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4 Chebyshevs Rule any sample, regardless of the
f.d.shape

• It is possible that very few of the measurements
  fall within 1 std. Dev. Of the mean
• At least ¾ of the measurements will fall within 2
  std dev of the mean (m-2s, m2s)
• At least 8/9 of the measurements will fall within
  3 std dev of the mean (m-3s, m3s)

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3 Empirical Rule frequency distributions are
mound shaped

• Apprx. 68 of the measurements will fall within 1
  std dev of the mean (m-s, ms)
• Approx. 95 of the measurements will fall within
  2 std dev of the mean (m-2s, m2s)
• Essentially all the measurements will fall within
  3 std dev of the mean (m-3s, m3s)

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Confidence Intervals and Levels 4

• Where is the population mean?
• Can narrow the range of possibilities if it is
  assumed
• 1. The sampling distribution of the means is
  normal
• 2. At least one of the means in the sampling
  distribution of sample means is identical to the
  population mean
• Hence, can infer that 95 of all possible
  sampling means in the sampling distribution fall
  within the range 44.16 to 45.40 (i.e. w/in 2 std
  dev)
• Picture, p. 438

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Confidence Intervals and Levels 4

• To construct confidence interval, need
• The standard error for the mean (std dev of samp
  dist of samp means)
• Mean for a particular sample (to represent the
  mean of the sampling distribution of the sample
  means)
• 95 of all values in a normal distribution will
  fall within 2 standard errors of the mean.
• Therefore, 5 of the sampling values fall outside
  that range
• Skills 3, p. 440
• SPSSconf. Int (p. 441)
• P. 442-43Interpretation of Confidence Interval

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• Z_(a/2) is the Z value with an area a/2 to its
  right (a100-CI)
• Confidence interval formulas, p. 445
• Example, p. 445
• Skills 4
• Confidence levels using SPSS P. 446
• P.449-50standard Error of proportions formula
  11.2, example
• P. 451 CI for specified levels formula 11.3,
  example
• Skills 5, skills 6,skills 7

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Homework Chapter 11

• Gen ex P. 461/ 1,3,4,6,9,11,13
• Hand in p. 462/ 8, 12 SPSS/ 1