WST121 PRACTICAL TEST – 2006

TOTAL: 30 MARKS:

INITIALS AND SURNAME

STUDENT NUMBER

SIGNATURE

INSTRUCTIONS:

• Use ONLY EXCEL for Section A and ONLY SAS for Section B.
• Answer all questions for Section A by using the data in the spreadsheet.
• Give all answers correctly up to at least 3 DECIMAL PLACES.
• NO CALCULATORS OR ANY OTHER CALCULATION DEVICES may be used.
• Although the test is open-book, NO SHARING OF NOTES IS ALLOWED.
• All other exam regulations apply.

SECTION A
NUMBER of EXCEL WORKBOOK

One general belief by observers in the business world is that taller men earn more money than shorter men.
In Spreadsheet Nr.1 the height (in cm) (x) and the salary (y) (in R1 000) of 100 MBA graduates are given.
Fit a straight line to the data and write down the following values:

a b

R2

(3)
SECTION B

Question 1 to Question 3 are written questions. Do only Question 4 in SAS.

Question 1

National Paper Company must purchase a new machine for producing cardboard boxes. The company must
choose between two machines, machine 1 and machine 2. Since the machines produce boxes of equal
quality, the company will choose the machine that produces the most boxes in a one-hour period. It is known
that there are substantial differences in the abilities of the company’s machine operators. Therefore National
Paper has decided to compare the machines using a paired difference experiment. The results for eight
randomly selected machine operators, producing boxes for an hour on one machine and then for an hour on
the other machine are as follows.

Operator 1 2 3 4 5 6 7 8
Machine 1 53 60 58 48 46 54 62 49
Machine 2 50 55 56 44 45 50 57 47

SAS Output 1
The MEANS Procedure
Analysis Variable : DIFF
N Mean Std Error t Value Pr > |t|
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
8 3.2500000 0.5261043 6.18 0.0005
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ

SAS Output 2
The TTEST Procedure
Statistics
Lower CL Upper CL Lower CL Upper CL
Variable N Mean Mean Mean Std Dev Std Dev Std Dev Std Err
MACHINE1-MACHINE2 8 2.006 3.25 4.494 0.9839 1.488 3.0286 0.5261

T-Tests
Variable DF t Value Pr > |t|
MACHINE1-MACHINE2 7 6.18 0.0005

(a) Complete the following SAS program so that it will produce EITHER SAS output 1 OR SAS output 2
(α=0.05) given above.

SAS program
DATA Q1;

INPUT MACHINE1 MACHINE2 @@;

CARDS;
53 50 60 55 58 56 48 44
46 45 54 50 62 57 49 47
;

(3)
(b) Use SAS Output 2 given on the previous page to write down a 95% confidence interval for µD, the
population mean difference.

(1)
(c) Test the claim that machine 1 produces significantly more boxes than machine 2. Use a significance
level of 5%. In your answer, only give the hypotheses, the p-value for the test and the rejection criteria.

(3)

Question 2

A study was undertaken in 2005 regarding the efficiency of recruitment companies. For each of 4 agencies
the number of positions filled per month, is given in the table below.

Month
Agency Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1 50 55 51 60 59 57 55 53 61 62 50 49
2 25 26 21 30 31 29 26 27 28 28 30 20
3 25 26 27 28 30 31 35 25 26 27 31 25
4 15 17 10 9 12 15 19 7 20 6 7 10

SAS Output
The GLM Procedure
Class Level Information
Class Levels Values
agency 4 1 2 3 4
Number of observations 48

The GLM Procedure

Dependent Variable: f
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 3 11541.75000 3847.25000 231.20 <.0001
Error 44 732.16667 16.64015
Corrected Total 47 12273.91667

R-Square Coeff Var Root MSE f Mean

0.940348 13.35629 4.079234 30.54167

Source DF Type I SS Mean Square F Value Pr > F

agency 3 11541.75000 3847.25000 231.20 <.0001

Source DF Type III SS Mean Square F Value Pr > F

agency 3 11541.75000 3847.25000 231.20 <.0001
 The GLM Procedure
Scheffe's Test for f
NOTE: This test controls the Type I experimentwise error rate.

Alpha 0.05
Error Degrees of Freedom 44
Error Mean Square 16.64015
Critical Value of F 2.81647
Minimum Significant Difference 4.8408

Means with the same letter are not significantly different.

Scheffe Grouping Mean N agency

A 55.167 12 1
B 28.000 12 3
B
B 26.750 12 2
C 12.250 12 4

(a) Complete the following SAS program so that it will produce (only) the output given above and on the
previous page.

SAS program

data q2;
input agency f @@;
cards;

1 50 1 55 1 51 1 60 1 59 1 57 1 55 1 53 1 61 1 62 1 50 1 49
2 25 2 26 2 21 2 30 2 31 2 29 2 26 2 27 2 28 2 28 2 30 2 20
3 25 3 26 3 27 3 28 3 30 3 31 3 35 3 25 3 26 3 27 3 31 3 25
4 15 4 17 4 10 4 9 4 12 4 15 4 19 4 7 4 20 4 6 4 7 4 10
;

(3)

(b) Test on a 5% level of significance whether the average number of positions filled per month differs
significantly for the four agencies. Only give the hypotheses, p-value and the decision that can be made.

(3)
(c) When doing a Scheffe pairwise comparison on a 5% level of significance, answer the following:

The average number of positions filled per month by agency 2 differs significantly from the average
number of positions filled per month by agency(s):

(1)

(d) Assume that the assumption of normality does not hold. Complete the following SAS program to test on
a 5% level of significance whether the median number of positions filled per month by the four agencies
differs significantly.

SAS program

data q2;
input agency f @@;
cards;
1 50 1 55 1 51 1 60 1 59 1 57 1 55 1 53 1 61 1 62 1 50 1 49
2 25 2 26 2 21 2 30 2 31 2 29 2 26 2 27 2 28 2 28 2 30 2 20
3 25 3 26 3 27 3 28 3 30 3 31 3 35 3 25 3 26 3 27 3 31 3 25
4 15 4 17 4 10 4 9 4 12 4 15 4 19 4 7 4 20 4 6 4 7 4 10
;

(3)
Question 3

The quality control manager of an automobile parts factory would like to know whether the quality of parts
produced (defective=def or acceptable=acc) depends on the day of the workweek. Random samples of 100
parts produced on each day of the week were selected and for each part it was determined whether it is
defective or acceptable. The results of this test can be seen in the SAS output below.

(a) Complete the following SAS Program to produce the output given below.

SAS program
data q3;
input day$ result$ freq @@;
cards;
Mon def 12 Tue def 7 Wed def 7 Thu def 10 Fri def 14
Mon acc 88 Tue acc 93 Wed acc 93 Thu acc 90 Fri acc 86
;

(4)

SAS Output
The FREQ Procedure
Table of result by day
result day
Frequency‚
Percent ‚
Row Pct ‚
Col Pct ‚Fri ‚Mon ‚Thu ‚Tue ‚Wed ‚ Total
ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ
acc ‚ 86 ‚ 88 ‚ 90 ‚ 93 ‚ 93 ‚ 450
‚ 17.20 ‚ 17.60 ‚ 18.00 ‚ 18.60 ‚ 18.60 ‚ 90.00
‚ 19.11 ‚ 19.56 ‚ 20.00 ‚ 20.67 ‚ 20.67 ‚
‚ 86.00 ‚ 88.00 ‚ 90.00 ‚ 93.00 ‚ 93.00 ‚
ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ
def ‚ 14 ‚ 12 ‚ 10 ‚ 7 ‚ 7 ‚ 50
‚ 2.80 ‚ 2.40 ‚ 2.00 ‚ 1.40 ‚ 1.40 ‚ 10.00
‚ 28.00 ‚ 24.00 ‚ 20.00 ‚ 14.00 ‚ 14.00 ‚
‚ 14.00 ‚ 12.00 ‚ 10.00 ‚ 7.00 ‚ 7.00 ‚
ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ
Total 100 100 100 100 100 500
20.00 20.00 20.00 20.00 20.00 100.00

Statistics for Table of result by day

Statistic DF Value Prob
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
Chi-Square 4 4.2222 0.3768
Likelihood Ratio Chi-Square 4 4.2331 0.3754
Mantel-Haenszel Chi-Square 1 4.0031 0.0454
Phi Coefficient 0.0919
Contingency Coefficient 0.0915
Cramer's V 0.0919

Sample Size = 500

(b) Use α=0.10 and test whether there is evidence of a significant relationship between quality of the items
produced and the day of the week.
In your answer, only give the hypotheses, the p-value for the test and the decision made.

(3)
Question 4

Use SAS to determine the answer to the following questions. Only write down your answer in the space
provided.

(a) Suppose Y~χ2(10). P (Y ≥ 8) =

(b) Suppose T~t(10). The 80th percentile of T =

(c) Suppose X~n(1500, 1602). P (1400 ≤ X ≤ 1700) =

(3)
[30]