UNIVERSITY OF SOUTH AFRICA
College of Science, Engineering and Technology
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
STA4820: Applied Statistics
Assignment 01 — Semester 1, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
STA4820
Module Code:
Applied Statistics
Module Name:
Assignment 01
Assignment:
2026
Due Date:
41
Total Marks:
Submitted in partial fulfilment of the requirements for STA4820 — UNISA 2026
,UNISA | STA4820 Assignment 01 – 2026
Question 1: Population, Sample, Parameter and Statistic (12 marks)
Question: A certain reaction was run several times using catalysts. The catalysts were sup-
posed to control the yield of an undesirable side product. 44 runs were selected, and 20 were
from catalyst A to control the yield.
a) What is the population of interest? (2)
b) What is the sample? (2)
c) What is the parameter? (2)
d) What is the statistic? (2)
e) Does the value 44 refer to the parameter or to the statistic? (2)
f) Is the value 20 a parameter or a statistic? (2)
1(a) Population of Interest
The population is the complete set of all observations or items about which conclusions are
to be drawn (Walpole, Myers and Myers, 2017:6).
Answer: The population of interest is all runs of the reaction using catalysts to con-
trol the yield of the undesirable side product – that is, every possible run that could ever be
conducted using these catalysts under the experimental conditions.
1(b) The Sample
A sample is a subset drawn from the population for observation and analysis (Montgomery
and Runger, 2018:8).
Answer: The sample consists of the 44 runs that were selected from the total population of
all reaction runs. These 44 runs are the actual observations collected for analysis.
1(c) The Parameter
A parameter is a numerical descriptive measure of a population. Because the entire popula-
tion is rarely observed, parameters are usually unknown (Walpole et al., 2017:7).
Answer: The parameter is the true proportion (or mean yield) of all runs in the entire
population of reaction runs that use catalyst A to control the undesirable side product yield.
Page 2 of 18
,UNISA | STA4820 Assignment 01 – 2026
This value describes the whole population, not just the 44 selected runs.
1(d) The Statistic
A statistic is a numerical descriptive measure computed from the sample data. It is used to
estimate the corresponding population parameter (Montgomery and Runger, 2018:9).
Answer: The statistic is the proportion (or count) of runs in the sample that used cat-
alyst A. Here, 20 out of 44 sampled runs used catalyst A. Expressed as a sample proportion:
20
p̂ = ≈ 0.4545 (i.e., approximately 45.45%)
44
This sample proportion estimates the unknown population parameter.
1(e) Does the value 44 refer to the parameter or the statistic?
Answer: The value 44 refers to the statistic (specifically, the sample size n). It counts
the number of runs selected from the population for observation. Since 44 is derived from
the sample and not from the entire population, it characterises the sample rather than the
population.
Key Distinction
Parameter vs. Statistic: A parameter describes the entire population (usually un-
known and fixed). A statistic describes the sample (known and variable from sample
to sample). The value 44 is the sample size – it belongs to the sample, not to the
population.
1(f ) Is the value 20 a parameter or a statistic?
Answer: The value 20 is a statistic. It is the count of runs from catalyst A within the
selected sample of 44 runs. Because it is computed from the sample and not from the full
population of all possible runs, it is a sample statistic, not a population parameter.
Page 3 of 18
,UNISA | STA4820 Assignment 01 – 2026
Implementation Insight
In summary: both 44 (total sample size) and 20 (number of catalyst A runs in the
sample) are statistics. They are both derived from the sample. The parameter would be
the corresponding true count or proportion across the entire population of all reaction
runs – a value that is unknown unless every possible run is observed.
Page 4 of 18
, UNISA | STA4820 Assignment 01 – 2026
Question 2: Graphical Description of Catalyst Data (6 marks)
Question: A certain reaction was run several times using each of two catalysts, A and B. The
catalysts were supposed to control the yield of an undesirable side product. Results, in units
of percentage yield, for 24 runs of catalyst A and 20 runs of catalyst B are as follows:
Table 1: Percentage Yield Results by Catalyst Rating
Rating Results (%)
1. Catalyst A 20
2. Catalyst B 35
3. Catalyst C 70
4. Catalyst D 40
5. Catalyst E 35
Draw a graph that describes the data. What does the graph tell you? (6)
2.1 Bar Chart of Catalyst Yield Results
A bar chart is appropriate here because the variable on the horizontal axis (catalyst rating)
is categorical, and the height of each bar represents the percentage yield (a quantitative mea-
sure) for each catalyst (Montgomery and Runger, 2018:22).
Percentage Yield by Catalyst
80
70
Percentage Yield (%)
60
40
40 35 35
20
20
0
A B C D E
Catalyst
Figure 1: Bar chart showing percentage yield (%) for each catalyst rating
Page 5 of 18
College of Science, Engineering and Technology
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
STA4820: Applied Statistics
Assignment 01 — Semester 1, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
STA4820
Module Code:
Applied Statistics
Module Name:
Assignment 01
Assignment:
2026
Due Date:
41
Total Marks:
Submitted in partial fulfilment of the requirements for STA4820 — UNISA 2026
,UNISA | STA4820 Assignment 01 – 2026
Question 1: Population, Sample, Parameter and Statistic (12 marks)
Question: A certain reaction was run several times using catalysts. The catalysts were sup-
posed to control the yield of an undesirable side product. 44 runs were selected, and 20 were
from catalyst A to control the yield.
a) What is the population of interest? (2)
b) What is the sample? (2)
c) What is the parameter? (2)
d) What is the statistic? (2)
e) Does the value 44 refer to the parameter or to the statistic? (2)
f) Is the value 20 a parameter or a statistic? (2)
1(a) Population of Interest
The population is the complete set of all observations or items about which conclusions are
to be drawn (Walpole, Myers and Myers, 2017:6).
Answer: The population of interest is all runs of the reaction using catalysts to con-
trol the yield of the undesirable side product – that is, every possible run that could ever be
conducted using these catalysts under the experimental conditions.
1(b) The Sample
A sample is a subset drawn from the population for observation and analysis (Montgomery
and Runger, 2018:8).
Answer: The sample consists of the 44 runs that were selected from the total population of
all reaction runs. These 44 runs are the actual observations collected for analysis.
1(c) The Parameter
A parameter is a numerical descriptive measure of a population. Because the entire popula-
tion is rarely observed, parameters are usually unknown (Walpole et al., 2017:7).
Answer: The parameter is the true proportion (or mean yield) of all runs in the entire
population of reaction runs that use catalyst A to control the undesirable side product yield.
Page 2 of 18
,UNISA | STA4820 Assignment 01 – 2026
This value describes the whole population, not just the 44 selected runs.
1(d) The Statistic
A statistic is a numerical descriptive measure computed from the sample data. It is used to
estimate the corresponding population parameter (Montgomery and Runger, 2018:9).
Answer: The statistic is the proportion (or count) of runs in the sample that used cat-
alyst A. Here, 20 out of 44 sampled runs used catalyst A. Expressed as a sample proportion:
20
p̂ = ≈ 0.4545 (i.e., approximately 45.45%)
44
This sample proportion estimates the unknown population parameter.
1(e) Does the value 44 refer to the parameter or the statistic?
Answer: The value 44 refers to the statistic (specifically, the sample size n). It counts
the number of runs selected from the population for observation. Since 44 is derived from
the sample and not from the entire population, it characterises the sample rather than the
population.
Key Distinction
Parameter vs. Statistic: A parameter describes the entire population (usually un-
known and fixed). A statistic describes the sample (known and variable from sample
to sample). The value 44 is the sample size – it belongs to the sample, not to the
population.
1(f ) Is the value 20 a parameter or a statistic?
Answer: The value 20 is a statistic. It is the count of runs from catalyst A within the
selected sample of 44 runs. Because it is computed from the sample and not from the full
population of all possible runs, it is a sample statistic, not a population parameter.
Page 3 of 18
,UNISA | STA4820 Assignment 01 – 2026
Implementation Insight
In summary: both 44 (total sample size) and 20 (number of catalyst A runs in the
sample) are statistics. They are both derived from the sample. The parameter would be
the corresponding true count or proportion across the entire population of all reaction
runs – a value that is unknown unless every possible run is observed.
Page 4 of 18
, UNISA | STA4820 Assignment 01 – 2026
Question 2: Graphical Description of Catalyst Data (6 marks)
Question: A certain reaction was run several times using each of two catalysts, A and B. The
catalysts were supposed to control the yield of an undesirable side product. Results, in units
of percentage yield, for 24 runs of catalyst A and 20 runs of catalyst B are as follows:
Table 1: Percentage Yield Results by Catalyst Rating
Rating Results (%)
1. Catalyst A 20
2. Catalyst B 35
3. Catalyst C 70
4. Catalyst D 40
5. Catalyst E 35
Draw a graph that describes the data. What does the graph tell you? (6)
2.1 Bar Chart of Catalyst Yield Results
A bar chart is appropriate here because the variable on the horizontal axis (catalyst rating)
is categorical, and the height of each bar represents the percentage yield (a quantitative mea-
sure) for each catalyst (Montgomery and Runger, 2018:22).
Percentage Yield by Catalyst
80
70
Percentage Yield (%)
60
40
40 35 35
20
20
0
A B C D E
Catalyst
Figure 1: Bar chart showing percentage yield (%) for each catalyst rating
Page 5 of 18
