1) A pediatrician’s office wanted to know whether parents were happier with their practice if they provide one waiting room for all patients, separate waiting rooms for sick and well children, or had no waiting room and families were shown directly to exam rooms. Families were randomly assigned to one of those three groups. Their scores on a satisfaction survey (points out of 10) are listed below.
| Shared (A) | Separate (B) | None (C) |
| 3 | 10 | 6 |
| 4 | 9 | 6 |
| 3 | 8 | 7 |
| 4 | 7 | 6 |
a) Can the office determine if there was a significant difference between the waiting room conditions (shared vs. separate vs. none) at
a = 0.05? Show all necessary components of a full hypothesis test, including a source table. (30 points)
b) Perform a Tukey’s HSD post-hoc test for the difference between the shared and separate conditions. Is this a significant difference? (5 points)
2) A hospital administrator wanted to know if the nurses at her hospital preferred one brand of stethoscope over another. She gave 3 nurses a different stethoscope to try out each week and asked them to rate their liking for that stethoscope on a scale of 1 to 5 (1 = hated it, 5 = loved it). Was there any difference in the nurses’ preference in brand (a = 0.05)? Show all necessary components of a full hypothesis test, including a source table. (35 points)
| Nurse | Littmann (A) | Prestige Medical (B) | ADC (C) |
| 1 | 5 | 3 | 1 |
| 2 | 4 | 2 | 2 |
| 3 | 3 | 4 | 3 |
3) A home gardener wanted to determine which combination of plant seeds and fertilizer would produce the best tomatoes. She planted 3 different tomato seeds and used 5 different types of fertilizer for each type of seed (15 combinations of seed and fertilizer total). She created a source table for the results of her ANOVA but unfortunately spilled coffee on it and blurred some of the cells.
| Source | SS | df | MS | F |
| Seed | 512.867 | 2 | 28.283 |
| Fertilizer | 449.467 | 4 | 112.367 |
| Seed*Fertilizer | 143.133 | 17.892 | 1.973 |
| Within | 136.000 | 9.067 |
| Total | 29 |
a) Fill in the missing cells. (15 points)
b) Which of the
F statistics are significant? Be sure to give the critical
F value(s) you used to determine this. (10 points)
c) What is the effect size for the main effect of fertilizer type? What size effect is this? (5 points)
Extra Credit 1: A journal article reports an ANOVA statistic of
F(1, 14) = 5.78,
p Extra Credit 2: When do you use
N in the Tukey HSD post-hoc test formula? When do you use
N’ instead? (1 point)