Question

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:


Groep / Group 1

Groep / Group 2

Groep / Group 3

Totaal / Total

Menu-aangedrewe / Menu-driven

Opdrag-aangedrewe / Command-driven

Mengsel / 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










Die volgende gedeeltelik voltooide ANAVA tabel is vir die bostaande data verkry. / 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 D in the observation table?

Answer 1

To solve for the total G (sum of all observations) and help you find D, we need to first calculate the total time taken by all secretaries across the three groups.

Let's find the total time for each group:

- **Group 1 (Menu-driven):**
- 12 + 16 + 10 + 12 + 10 + 16 = 76 minutes

- **Group 2 (Command-driven):**
- 14 + 10 + 14 + 12 + 10 + 14 = 84 minutes

- **Group 3 (Mixed):**
- 10 + 8 + 10 + 10 + 8 + 4 = 60 minutes

Now, we'll sum these totals to find the grand total (G):

\[
G = 76 + 84 + 60 = 220 \text{ minutes}
\]

Next, we need to find the value of \( N \), which is the total number of observations (secretaries). In the problem, each group has 6 secretaries, so:

\[
N = n_1 + n_2 + n_3 = 6 + 6 + 6 = 18
\]

Now, we need to find the values of \( n_1 \), \( n_2 \), and \( n_3 \):

- \( n_1 = 6 \) for Group 1 (Menu-driven)
- \( n_2 = 6 \) for Group 2 (Command-driven)
- \( n_3 = 6 \) for Group 3 (Mixed)

Thus:

\[
n_1 = 6, \quad n_2 = 6, \quad n_3 = 6
\]

So, we have:

- \( N = 18 \)

Now we can summarize our calculated values:

- \( R_1 = 76 \)
- \( R_2 = 84 \)
- \( R_3 = 60 \)
- \( G = 220 \)

Thus:

- \( D = G = 220 \)

To summarize:

The value of \( D \) in the observation table is **220**.