The science of ergonomics studies the influence of “human factors” in technology, i.e. how human beings relate to and work with machines. With widespread use of computers for data processing, computer scientists and psychologists are getting together to study human factors. One typical study investigates the productivity of secretaries with different word processing programs. An identical task was given to 18 secretaries, randomly allocated to three groups. Group 1 used a menu-driven program. Group 2 used a command-driven program, and Group 3 used a mixture of both approaches. The secretaries all had about the same level of experience, typing speed, and computer skills. The time (in minutes) taken to complete the task was observed. The results were as follows:

Question

Group 1
Group 2

Group 3

Total

Menu-driven

Command-driven

Mixed



12

14

10



16

10

8



10

14

10



12

12

10



10

10

8



16

14

4



n1 =

n2 = A

n3 =

N = B

R1 =

R2 =

R3 = C

G = D

The following partially completed ANOVA table was obtained for the above data.

ANOVA table:

Source

SS

df

MS

Fcalc

Ftab

Treatments

H

J

34.8889

M

P

Error

84

15

L



Total

I

K







What is the value of A in the observation table?

Answer 1

To find the value of \( A \), which represents the sample size \( n_2 \) (the number of observations in Group 2), we first need to determine how many observations were made in each group based on the data provided.

Let's break down the provided data into three groups:

Group 1 (Menu-driven):

1. 12
2. 16
3. 10
4. 12
5. 10
6. 16

This gives us \( n_1 = 6 \).

Group 2 (Command-driven):

1. 14
2. 10
3. 14
4. 12
5. 10
6. 14

This gives us \( n_2 = 6 \) (which is the value of \( A \)).

Group 3 (Mixed):

1. 10
2. 8
3. 10
4. 8
5. 4
6. 10

This gives us \( n_3 = 6 \).

Now we can summarize the sizes of each group:

• \( n_1 = 6 \)
• \( n_2 = 6 \) (this is \( A \))
• \( n_3 = 6 \)

Total number of observations \( N \):

The total number of observations is given by: \[ N = n_1 + n_2 + n_3 = 6 + 6 + 6 = 18 \]

Now let's summarize the results that we have:

• \( n_1 = 6 \)
• \( n_2 = 6 \) (value of \( A \))
• \( n_3 = 6 \)
• \( N = 18 \)

Thus, the value of \( A \) is:

\[ \boxed{6} \]