QUESTION 1 [12]

1.1 Indicate whether the following statements are True or False. Give reasons for your answer.

a) For this module, the level of significance is always given as 0,005. (2)

b) A Type I error is made by rejecting the null hypothesis when it is in fact true. (2)

c) If you get a negative value for the F-test, this means the test statistic falls inside the rejection area. (2)

1.2 State whether the following alternative hypotheses are nondirectional or directional. Justify your answer.

a) There is a significant difference between the performance of students in Assessment 01 and  Assessment 02. (2)

b) Participation in e-tutor sessions is positively related to student performance of IOP2601 students. (2)

c) The performance of IOP2601 students who attend tutorial classes is higher than the performance of IOP2601 students who do not attend tutorial classes. (2)

QUESTION 2 [15]

The Student Support Department collected data from students registered for IOP2601 in 2023. They wanted to know if there is a difference in the success (performance) in the module between students with a mathematics background and those without a mathematics background.

Table 1 provides the performance scores obtained from the 102 randomly selected IOP2601 students.

Table 1
Statistical Data

Mathematics background N x s2
With mathematics background 51 5,34 1,28

Without mathematics background 51 4,94 1,29

2.1 Formulate an appropriate null hypothesis (H0) in symbol and in words. (2)

2.2 Formulate an appropriate alternative hypothesis (H1) in symbol and in words. (2)

2.3 Is the hypothesis test in this question one-tailed or two-tailed? (1)

2.4 Assuming that the data are normally distributed, select an appropriate statistical test and calculate the test statistic using the information provided in Table 1. Show ALL calculations. (3)

2.5 Determine the degrees of freedom. (2)

2.6 Using your answers to questions 2.3 and 2.5, determine the critical value for the test for a significance level of 1% (0,01). (1)

2.7 Interpret the results in terms of the rejection or non-rejection of the null hypothesis and justify your answer. (2)

2.8 Interpret your rejection or non-rejection of the null hypothesis in plain language, in terms of the original problem statement. (2)

A Unisa researcher wants to know if students’ perceptions of continuous assessment change as they progress in the semester. The researcher randomly selected five students who registered for a module that has continuous assessment and measured their perceptions at the beginning, in the middle and at the end of the semester.

The scores obtained from the survey are provided in Table 2 below.

Table 2
Perceptions of Continuous Assessment Scores

Beginning (X1) Middle (X2) End (X3)
2 3 3

3 3 5

1 2 4

3 4 5

2 4 6

ƩX1 = 11 ƩX2 = 16 ƩX3 = 23
𝑋̅1 = 2,2 𝑋̅2 = 3,2 𝑋̅3 = 4,6
Totals: Ʃ𝑋̅ = 3,33
X = 50
X 2 = 192

The researcher’s question was as follows: Is there a significant difference in the students’ perceptions of continuous assessment as they progress in the semester?
Stated differently, the following null hypothesis needs to be tested:
H0: 1 = 2 = 3 with  = 0,01

3.1 Choose an appropriate test statistic to test this hypothesis and calculate the test statistic. Present your answers in a summary table. (8)

3.2 Determine the critical value that will help you decide whether or not you should reject the null hypothesis at  = 0,01. (1)

3.3 Do you reject the null hypothesis? (1)

3.4 Interpret your findings in terms of the original problem statement. (2)

Study the information provided in Table 3 and thereafter, answer the questions that follow.

Table 3
Methods of Instruction

Sum of
Squares DF

Mean Square
F

Sig.
Between Groups 1183,189 3 394,396 3,728 0,012

Within Groups 32369,250 306 105,782
Total 33552,439 309

Research question: Is there a significant difference between the performance of the students in
IOP2601 according to the three methods of instruction, namely video, online class and self-study?

4.1 Based on the research question above, state the null hypothesis in words. (1)

4.2 Based on the ANOVA above, do you reject the null hypothesis?(1)

4.3 Interpret your rejection or non-rejection of the null hypothesis in plain language, in terms of the original research question. (2)

QUESTION 5 [7]

A human resources senior researcher is interested in discovering if there is a difference in preferences of administrative and academic employees in terms of the going back-to-the-office arrangement. The researcher is conducting this research after all 270 employees of this institution have been working from home permanently for a period of three years.

Table 4 below provides you with preference scores obtained from the poll sent to both administrative and academic employees.

Table 4
Preference Scores
Category In office 5 days per week

In office once per week

In office once per month

After analysing the responses, the chi square value was = 11,82.

5.1 Compile a contingency table to represent the information given in Table 4. (3)

5.2 Determine the degree of freedom. (1)

5.3 Determine the critical value at a significance level of  = 0,05. (1)

5.4 Indicate your rejection or non-rejection of the null hypothesis and then interpret it in plain language, in terms of the original research problem.

Answers to Above Question on Statistics

Answer 1: The statement is false because the level of significance, often denoted as α (alpha), is not always given as 0.005.

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