Section 3.2 Solutions

(Note: Arrows should be drawn between the pieces of each experiment diagram.)

3.10

The experimental units are the participating middle schools. The factors are the “physical activity intervention” (PAI) and the “nutrition intervention” (NI). The four treatments are (PAI and NI), (PAI and no NI), (no PAI and NI), and (no PAI and no NI). The response variables are physical activity and lunchtime consumption of fat.

3.14

Group 1 Treatment 1

(10 subjects) (potent cigarettes)

20 subjects random Compare work output

assignment and earnings

Group 2 Treatment 2

(10 subjects) (weak cigarettes)

To do the randomization:

Label the subjects 1-20 (going down the columns). From Table B, line 131, Group 1 includes: 05, 19, 04, 20, 16, 18, 07, 13, 02, and 08. Thus, Decker, Travers, Chen, Ullmann, Quinones, Thompson, Fluharty, Lucero, Afifi, and Gerson are in Group 1 and will receive potent cigarettes.

3.18

The treatments are shown in the table below.

	Factor B – Fraction on Sale
Factor A – Discount Level	25%	50%	75%	100%
20%	Treatment 1	Treatment 2	Treatment 3	Treatment 4
40%	Treatment 5	Treatment 6	Treatment 7	Treatment 8
60%	Treatment 9	Treatment 10	Treatment 11	Treatment 12
80%	Treatment 13	Treatment 14	Treatment 15	Treatment 16

The partial design is shown below.

To do the randomization:

Label the subjects 1-80. From Table B, line 133, Group 1 includes: 45, 74, 04, 18, 07.

Group 1 Treatment 1

(5 subjects) (20%, 25%)

Group 2 Treatment 2

(5 subjects) (20%, 50%)

Group 3 Treatment 3

(5 subjects) (20%, 75%)

80 subjects random Group 4 Treatment 4 Compare attractiveness

assignment (5 subjects) (20%, 100%) ratings

Group 5 Treatment 5

(5 subjects) (40%, 25%)

Group 6 Treatment 6

(5 subjects) (40%, 50%)

Group 7 Treatment 7

(5 subjects) (40%, 75%)

.

.

.

.

Group 16 Treatment 7

(5 subjects) (80%, 100%)

3.23

The second option is a well-designed experiment, including control, (hopefully) randomization, and many replications. Hence, this experiment will isolate the effect of the bee pollen. In the first option, the women aren’t matched on all possible variables that may affect colon health, hence the effect of the bee pollen will be confounding with other variables such as dietary habits, exercise habits, and lifestyle choices.

3.25

1. The design is randomized if subjects are randomly assigned a treatment, double-blind if both the subject and the researcher are unaware of which treatment is given, and placebo-controlled if a sugar-pill (placebo) is used to control for the psychological effect of taking medicine.

2. The design in shown in the diagram below.

Group 1 Treatment 1

(98 subjects) (Saint-John’s wort)

200 subjects random Compare the change

assignment in HRSD

Group 2 Treatment 2

(102 subjects) (placebo)

3.34

1. This is a block experimental design (the blocking variable is running status).

2. The design is shown in the diagram below (supposing there are 100 runners and 100 non-runners).

Group 1 Treatment 1

(50 runners) (Vitamin C)

runners random

(100) assignment compare number of

infections

Group 2 Treatment 2

(50 runners) (placebo)

subjects

(200)

Group 1 Treatment 1

(50 non-runners) (vitamin C)

nonrunners random

(100) assignment compare number of

infections

Group 2 Treatment 2

(50 non-runners) (placebo)

3. The results observed in this study would rarely occur by chance if vitamin C were ineffective.