FEEDBACK ON ASSESSMENT 2
This is the second assessment that you had to submit. It contributes 25% towards your final mark. See
page 10 in Tutorial Letter IOP2601/101/3/2023 for details on how to calculate your final mark.
A full memorandum is provided here. Compare your answers with the following memorandum and make
sure that you understand the rest of the descriptive statistics and inferential statistics that are covered in
this assignment.
REMEMBER:
● Always give the formula (computational formula) for the computation asked – in most cases you
will receive a mark for it.
● Read the questions carefully.
● Do computations with the variable asked. You will not receive any marks if you do the
computations correctly, but with the wrong variable.
QUESTION 1 (11)
Thabo and his friend Sipho entered a lucky draw and can win a laptop as the first prize and a cellphone
as the second prize, from Unisa. Thabo sent through 60 entry forms, while Sipho sent through 40. The
report from the competition administrators is that 200 entries qualified, and both Thabo and Sipho qualified.
Use this information to answer the following questions:
1.1 What is the probability that Thabo will win first prize? (2)
p(Thabo)o) = 60/200
= 0,30
1.2 What is the possibility that Sipho will win first prize? (2)
p(Sipho) = 40/200
= 0,20
1.3 If Thabo wins first prize, what is the probability that Sipho will win second prize?
=====+++++
(The first prize-winning entry is not put back in the container.) (2)
p(Sipho) = 40/199
= 0,20100
= 0,20
1.4 If Sipho wins first prize, what is the probability that Thabo will win second prize?
(The first prize-winning entry is not put back in the container.) (2)
p(Thabo) = 60/199
= 0,30150
= 0.30
, 1 IOP2601/Ass 02/Sem 1 2023_Feedback
1.5 What is the probability that Thabo and Sipho will win first and second prize? (3)
p(Thabo) x p(Sipho) = 60/200 x 40/199
= 0,30 x 0,20
= 0,06
p(Sipho) x p(Thabo) = 40/200 x 60/199
= 0,20 x 0,30
= 0,06
p(Thabo & Sipho) = 0,06 + 0,06
= 0,12
= 0.12
=
QUESTION 2 (20)
A study conducted by an American researcher showed that in most companies, employees who work from
home perform better than those that work in the office. A researcher in your company wanted to test the
validity of this study in an African context by firstly assessing the relationship between working from home
(X) and performance (Y), and she found the following:
N = 10 ƩX = 72 ƩX2 =534 ƩY = 95 ƩY2 = 961 ƩXY = 682
ƩXƩY = 72 x 95 = 6840
(ƩX)2 = (72)2 = 5184
(ƩY)2 = (95)2 = 9025
2.1 Calculate the relationship between working from home and performance scores. (3)
𝑁Σ𝑋𝑌 − Σ𝑋Σ𝑌
=
√[𝑁Σ𝑋 2 − (Σ𝑋)2 ][𝑁Σ𝑌 2 − (Σ𝑌 )2 ]
10(682)−(72)(95)
=
√[10(534)− (72)2 ][10(961)− (95)2 ]
6820− 6840
=
√[5340− 5184][9610−9025]
−20
=
√91260
−20
=
302,092
= -0,066
= - 0,07
2.2 Interpret the correlation coefficient. (2)
A weak negative correlation
2.3 What can you deduce about the nature of the relationship between working from home and
performance scores? (1)
The lower the WORKING FROM HOME scores the higher the PERFORMANCE scores.
OR
The more the employees WORK FROM HOME, the lower their scores in terms of
PERFORMANCE.
This is the second assessment that you had to submit. It contributes 25% towards your final mark. See
page 10 in Tutorial Letter IOP2601/101/3/2023 for details on how to calculate your final mark.
A full memorandum is provided here. Compare your answers with the following memorandum and make
sure that you understand the rest of the descriptive statistics and inferential statistics that are covered in
this assignment.
REMEMBER:
● Always give the formula (computational formula) for the computation asked – in most cases you
will receive a mark for it.
● Read the questions carefully.
● Do computations with the variable asked. You will not receive any marks if you do the
computations correctly, but with the wrong variable.
QUESTION 1 (11)
Thabo and his friend Sipho entered a lucky draw and can win a laptop as the first prize and a cellphone
as the second prize, from Unisa. Thabo sent through 60 entry forms, while Sipho sent through 40. The
report from the competition administrators is that 200 entries qualified, and both Thabo and Sipho qualified.
Use this information to answer the following questions:
1.1 What is the probability that Thabo will win first prize? (2)
p(Thabo)o) = 60/200
= 0,30
1.2 What is the possibility that Sipho will win first prize? (2)
p(Sipho) = 40/200
= 0,20
1.3 If Thabo wins first prize, what is the probability that Sipho will win second prize?
=====+++++
(The first prize-winning entry is not put back in the container.) (2)
p(Sipho) = 40/199
= 0,20100
= 0,20
1.4 If Sipho wins first prize, what is the probability that Thabo will win second prize?
(The first prize-winning entry is not put back in the container.) (2)
p(Thabo) = 60/199
= 0,30150
= 0.30
, 1 IOP2601/Ass 02/Sem 1 2023_Feedback
1.5 What is the probability that Thabo and Sipho will win first and second prize? (3)
p(Thabo) x p(Sipho) = 60/200 x 40/199
= 0,30 x 0,20
= 0,06
p(Sipho) x p(Thabo) = 40/200 x 60/199
= 0,20 x 0,30
= 0,06
p(Thabo & Sipho) = 0,06 + 0,06
= 0,12
= 0.12
=
QUESTION 2 (20)
A study conducted by an American researcher showed that in most companies, employees who work from
home perform better than those that work in the office. A researcher in your company wanted to test the
validity of this study in an African context by firstly assessing the relationship between working from home
(X) and performance (Y), and she found the following:
N = 10 ƩX = 72 ƩX2 =534 ƩY = 95 ƩY2 = 961 ƩXY = 682
ƩXƩY = 72 x 95 = 6840
(ƩX)2 = (72)2 = 5184
(ƩY)2 = (95)2 = 9025
2.1 Calculate the relationship between working from home and performance scores. (3)
𝑁Σ𝑋𝑌 − Σ𝑋Σ𝑌
=
√[𝑁Σ𝑋 2 − (Σ𝑋)2 ][𝑁Σ𝑌 2 − (Σ𝑌 )2 ]
10(682)−(72)(95)
=
√[10(534)− (72)2 ][10(961)− (95)2 ]
6820− 6840
=
√[5340− 5184][9610−9025]
−20
=
√91260
−20
=
302,092
= -0,066
= - 0,07
2.2 Interpret the correlation coefficient. (2)
A weak negative correlation
2.3 What can you deduce about the nature of the relationship between working from home and
performance scores? (1)
The lower the WORKING FROM HOME scores the higher the PERFORMANCE scores.
OR
The more the employees WORK FROM HOME, the lower their scores in terms of
PERFORMANCE.
