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Introductory Statistics

Chapter Review

Introductory StatisticsChapter Review

Chapter Review

10.1 Two Population Means with Unknown Standard Deviations

Two population means from independent samples where the population standard deviations are not known

  • Random Variable: X ¯ 1 − X ¯ 2 X ¯ 1 − X ¯ 2 = the difference of the sampling means
  • Distribution: Student's t-distribution with degrees of freedom (variances not pooled)

10.2 Two Population Means with Known Standard Deviations

A hypothesis test of two population means from independent samples where the population standard deviations are known will have these characteristics:

  • Random variable: X ¯ 1 − X ¯ 2 X ¯ 1 − X ¯ 2 = the difference of the means
  • Distribution: normal distribution

10.3 Comparing Two Independent Population Proportions

Test of two population proportions from independent samples.

  • Random variable: p ^ A – p ^ B = p ^ A – p ^ B = difference between the two estimated proportions
  • Distribution: normal distribution

10.4 Matched or Paired Samples

A hypothesis test for matched or paired samples (t-test) has these characteristics:

  • Test the differences by subtracting one measurement from the other measurement
  • Random Variable: x ¯ d x ¯ d = mean of the differences
  • Distribution: Student’s-t distribution with n – 1 degrees of freedom
  • If the number of differences is small (less than 30), the differences must follow a normal distribution.
  • Two samples are drawn from the same set of objects.
  • Samples are dependent.
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