FEEDBACK ON ASSESSMENT 3
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 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 [6]
Indicate whether the following statements are True or False.
1.1 The single-sample t-test is used when you have a single set of scores and are investigating whether
the mean of this sample equals a known mean.
True
1.2 A Type II error is made by rejecting the null hypothesis when it is in fact true.
False
1.3 ANOVA allows us to test for differences between more than two group means and to examine the
effects of more than one independent variable.
True
1.4 ANOVA is an acronym for analysis of variables.
False
1.5 A Type I error is made by not rejecting the null hypothesis when it is false.
False
1.6 A Chi-Square test is typically used to test for association between two categorical variables.
True
QUESTION 2 [10]
2.1 Explain the difference between a null hypothesis and an alternative hypothesis. Your explanation
must include an example. (NB: Use your own words to avoid plagiarising). (4)
Answer:
A null hypothesis is a negative statement about a possible difference between the variables that you want
to study. Example: researchers would state that there is no difference between the variables that they are
researching, or they might say that both variables under study are equal.
An alternative hypothesis is the opposite of the null hypothesis since it is not negative but affirmative.
Example, researchers would state that there is a difference between the variables that they are measuring.
[TURN OVER]
, 2
IOP2601/Assignment 03/Semester 1/2023 Feedback
2.2 State whether the following alternative hypothesis are nondirectional or directional. Justify your
answer. (6)
a) H1: μ1 > μ2
Directional: Because one variable is larger than the other (>)
b) H1: μA < μB
Directional: one variable is smaller than the other (<)
c) H1: μA ≠ μB
Nondirectional: the two variables are not equal (≠), meaning that they somehow differ.
QUESTION 3 [15]
A research scholar collected data from a small coal mining company that recently opened a plant in
Mpumalanga. She wants to know if there is a difference in the productivity of employees working a day
shift in comparison to those working during the night.
Table 1 provides the productivity scores she obtained from the ten (10) randomly selected employees from
each shift.
Table 1
Productivity Scores
Day Shift Night Shift
9 7
9 6
8 5
6 7
7 4
6 6
5 6
6 3
6 7
7 5
The scholar decided on a level of significance of α = 0,01.
3.1 Formulate an appropriate null hypothesis (H0) in symbol and in words. (2)
H0 : µDayShift = µNightShift
There is no significant difference in the productivity of employees working a day shift in
comparison to those working during the night.
3.2 Formulate an appropriate alternative hypothesis (H1) in symbol and in words. (2)
H1: µDayShift ≠ µNightShift
There is a significant difference in the productivity of employees working a day shift
in comparison to those working during the night.
3.3 Is the hypothesis test one-tailed or two-tailed? (1)
Two-tailed
3.4 Assuming that the data are normally distributed, select an appropriate statistical test and calculate
the test statistic using the information provided in Table 2 below. Show ALL calculations. (3)
[TURN OVER]
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 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 [6]
Indicate whether the following statements are True or False.
1.1 The single-sample t-test is used when you have a single set of scores and are investigating whether
the mean of this sample equals a known mean.
True
1.2 A Type II error is made by rejecting the null hypothesis when it is in fact true.
False
1.3 ANOVA allows us to test for differences between more than two group means and to examine the
effects of more than one independent variable.
True
1.4 ANOVA is an acronym for analysis of variables.
False
1.5 A Type I error is made by not rejecting the null hypothesis when it is false.
False
1.6 A Chi-Square test is typically used to test for association between two categorical variables.
True
QUESTION 2 [10]
2.1 Explain the difference between a null hypothesis and an alternative hypothesis. Your explanation
must include an example. (NB: Use your own words to avoid plagiarising). (4)
Answer:
A null hypothesis is a negative statement about a possible difference between the variables that you want
to study. Example: researchers would state that there is no difference between the variables that they are
researching, or they might say that both variables under study are equal.
An alternative hypothesis is the opposite of the null hypothesis since it is not negative but affirmative.
Example, researchers would state that there is a difference between the variables that they are measuring.
[TURN OVER]
, 2
IOP2601/Assignment 03/Semester 1/2023 Feedback
2.2 State whether the following alternative hypothesis are nondirectional or directional. Justify your
answer. (6)
a) H1: μ1 > μ2
Directional: Because one variable is larger than the other (>)
b) H1: μA < μB
Directional: one variable is smaller than the other (<)
c) H1: μA ≠ μB
Nondirectional: the two variables are not equal (≠), meaning that they somehow differ.
QUESTION 3 [15]
A research scholar collected data from a small coal mining company that recently opened a plant in
Mpumalanga. She wants to know if there is a difference in the productivity of employees working a day
shift in comparison to those working during the night.
Table 1 provides the productivity scores she obtained from the ten (10) randomly selected employees from
each shift.
Table 1
Productivity Scores
Day Shift Night Shift
9 7
9 6
8 5
6 7
7 4
6 6
5 6
6 3
6 7
7 5
The scholar decided on a level of significance of α = 0,01.
3.1 Formulate an appropriate null hypothesis (H0) in symbol and in words. (2)
H0 : µDayShift = µNightShift
There is no significant difference in the productivity of employees working a day shift in
comparison to those working during the night.
3.2 Formulate an appropriate alternative hypothesis (H1) in symbol and in words. (2)
H1: µDayShift ≠ µNightShift
There is a significant difference in the productivity of employees working a day shift
in comparison to those working during the night.
3.3 Is the hypothesis test one-tailed or two-tailed? (1)
Two-tailed
3.4 Assuming that the data are normally distributed, select an appropriate statistical test and calculate
the test statistic using the information provided in Table 2 below. Show ALL calculations. (3)
[TURN OVER]
