Stat 401 A: HW 5 answers (corrected)
Problems 1-3: 2 points each, one for eu, one for ou.
1) eu: car or questionnaire (they are the same because one questionnaire per car)
ou: car or questionnaire
2) eu: neighborhood (or school)
ou: student
3) eu: neighborhood (or school)
ou: school
4) 3 pts. 2 for eus, one for ou.
eu: there are two in this study: room (assigned to vaccinate or not); pig (assigned to sacrifice time)
ou: pig
Note for Q1-Q4: Many of you confused the obs. unit with the response and that is why you were marked
off. Problems 2 and 3 illustrate why you care about the difference. The response variable is the same in
both (reading score). 2 has problems with non-independence: more students (ou) than schools (eu). 3
is just fine; the ou (school) is the eu (school).
5) 5 pts. -4 if missed the subsampling and analyzed all 50 obs
a) 1 pt. a decrease of 37.4% (this is only result that is the same for all 50 obs or the 10 means)
b) 1 pt. 6.6% calculated from the 10 means. 2.9% was calculated from 50 obs.
c) 1 pt. 8 df.
d) 2 pt. (-22.2, -52.0) or rounded to (-22, -52) using Kelley’s rule. Also acceptable to say that the 95%
confidence is a decrease of (22, 52).
Note: If you analyzed all 50 obs., you have the wrong sd and df, so parts b, c, and d are wrong.
6) 6 pts.
a) 2 pts: bumblebee queen (type 1): mean 16.2, sd 10.0; honeybee worker (type 2): mean 35.8, sd 23.2
b) 2 pts: (-1 if made a box plot of the observations, not of the residuals)
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
1
2
c) 1pt: no issues. spreads look similar in the box plot. ratio of variances is 2.32, less than the 10 that I
consider an issue
d) 1 pt: no issues. distributions look reasonably symmetric in the box plot.
Note: Looking at the two sample variances (or sample sd’s) and finding that they are different values
does not tell you that the population variances are not equal. The assumption is about the population
variances. The two sample variances are likely to differ even when the population variances are the
same.