Assignment Task

Question 1

Indicate whether the following statements are True or False.

• 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.
• A Type II error is made by rejecting the null hypothesis whena it is in fact true.
• ANOVA allows us to test for differences between more than two group means and to examine the effects of more than one independent variable.
• ANOVA is an acronym for analysis of variables.
•  A Type I error is made by not rejecting the null hypothesis when it is false. 1.6 A Chi-Square test is typically used to test for association between two categorical variables.

Question 2

• State whether the following alternative hypothesis are nondirectional or Justify your answer. 
• Explain the difference between a null hypothesis and an alternative Your explanation must include an example. (NB: Use your own words to avoid plagiarising).
  • H ₁ : μ ₁ > μ ₂
  • H ₁ : μ _A < μ _B
  • H _1: μ _A ≠ μ _B

Question

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 the night shift.

Table 1 provides the productivity scores she obtained from the ten (10) randomly selected employees from each shift.

The research scholar decided on a level of significance of α = 0,01.

• Formulate an appropriate null hypothesis ( H ₀ ) in symbol and in (2)
• Formulate an appropriate alternative hypothesis ( H ₁ ) in symbol and in (2)
• Is the hypothesis test in this question one-tailed or two-tailed? (1)
• 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.

Statistical Data

• Determine the degrees of (2)
• Using your answers in questions 3 and 3.5, determine the critical value for the test for a significance level of 1% (0,01) . 
• Interpret the results in terms of the rejection or non-rejection of the null hypothesis and (2)
• Interpret your rejection or non-rejection of the null hypothesis in plain language, in terms of the original problem statement.

Question 4

A Unisa researcher wants to know if students’ attitude towards proctoring tools changes as they progress in the year. The researcher randomly selected five students who were using the proctoring tools and measured their attitudes towards the tools at the beginning, in the middle, and at the end of the year using the Attitude on Proctoring Survey (APS).

The scores obtained from the survey are provided in Table 3 below.

Proctoring Survey Scores

The researcher’s question was as follows: Is there a significant difference in the students’ attitude towards proctoring tools at the beginning, in the middle, and at the end of the year?

Or, stated differently, the following null hypothesis needs to be tested:

H ₀ : m ₁ = m ₂ = m ₃ with a = 0,05

• Choose an appropriate test statistic to test this hypothesis and calculate the test statistic. Present your answers in a summary (8)
• Determine the critical value which will help you to decide whether or not you should reject the null hypothesis at a = 0,05. (1)
• Do you reject the null hypothesis? (1)
• Interpret your findings in terms of the original problem statement.

Question 5

Study the computer output of an ANOVA, calculated using SPPS software programme, by a researcher who wanted to determine if the three different ethnic groups of employees working at ABC Logistics differed in terms of their productivity at work. A level of significance of a = 0,05 was used.

Based on the information provided, is there a significant difference between the three ethnic groups in terms of their productivity at work? Write your conclusion in terms of the problem statement in a full sentence.

Question 6

A human resource senior researcher is interested to know if there is a difference in preferences of administrative and academic employees in terms of the going back-to-the-office arrangement. This comes after all 250 employees of this institution had fully worked from home for a period of three years.

Table 5 below provides you with preference scores obtained from the poll sent to both administrative and academic employees.

Preference Scores

After the analysis of the responses was done, the chi square value was = 5,09 .

• Compile a contingency table to represent the information given in Table 5.

• Determine the degree of freedom.

  Determine the critical value at a significance level of a = 0,05