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: = 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 (typically approximated with the sample standard deviations) will have these characteristics:
- Random variable: = 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: difference between the two estimated proportions
- Distribution: normal distribution
10.4 Matched or Paired Samples (Optional)
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: = 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.