Statistics · Module 6
Answers and explanations · Separate variation in people from uncertainty in an average
Compare these references after your own attempt. You can read them at any time; they do not record a live model or vendor run.
Statistics · Module 6
Compare these references after your own attempt. You can read them at any time; they do not record a live model or vendor run.
6A. SE=6/√9=2 minutes; at n=36, SE=6/6=1 minute. The individual SD is still assumed to be 6. The estimate's repeated-sample variability shrinks because more independent outcomes are averaged, not because individual outcomes become less variable.
6B. Three of nine means equal 4, giving 1/3. Means at least 5 occur in (4,6), (6,4), (6,6), giving 3/9=1/3. The population mean is fixed at 4 in the specified finite population. These probabilities concern random samples and their means, not uncertainty about that known population mean.
6C. Repeats may share the same underlying participant value or measurement condition. Independence has not been established, and duplicate or correlated measurements do not supply the information of new independent participants. Repeats can improve some measurement estimates, but a suitable design/model must account for within-unit dependence.