Question 1 [28 Marks]

Read the fictitious scenario below and answer the question(s) which follow:

You are an entrepreneur looking to invest in a newly developed residential area. You are interested in investing in a grocery store such as Checkers, Pick n Pay, or Spar, which offer franchising deals. You need to decide which franchise will offer the best return on investment. There is currently no data on shopper behaviour related to the specific area you want to invest in. You managed to source a sample of secondary data, as seen in Table 1.1 below, of a survey done of the shopping behaviour of 30
shoppers in a similar area with a Checkers, Pick n Pay, and Spar.

Table 1.1 Sample data set of shoppers

Coding key:

• C# = Customer number(1-30).
• St = Store (1= Checkers; 2 = Pick n Pay; 3 = Spar)
• V# = Number of Visits (1-6 visits to a particular store)
• SpR = Spend in Rands (1= 400-600); 2 = 601-800; 3 = 801-1000; 4= 1001-
1200; 5 = 1201-1400; 6 = 1401- 1600; 7= 1601-1800; 8 = 1801-1900; 9 =
1901- 2000; 10 = 2001- 2201
• Fs = Family size (1-5 persons in the home)
• Age = Age
• Gen = Gender (1 = Female; 2 = Male)

Required:

In Excel, use the appropriate statistical technique to present a summary output and describe the characteristics of your dataset in Table 1.1. (12 marks)

Suggest at least three (3) critical questions that the analysis of the data has managed to answer. Also, suggest three (3) questions or aspects that the data analysis could not answer and are not yet clear and will need further investigation before a final decision to invest or not can be made. Use examples from the data set in Table 1.1 above to illustrate. (3×2=6 marks)

Assume that you, as an investor/entrepreneur, wish to focus on specific variables in the data set Table 1.1 for further investigation and analysis. However, to do this, you first need to show that your variables approximate a normal distribution.

Required:

In Excel, extract the variables SpR = Spend in Rands (1= 400-600); 2 = 601- 800; 3 = 801-1000; 4= 1001-1200; 5 = 1201-1400; 6 = 1401- 1600; 7= 1601-
1800; 8 = 1801-1900; 9 = 1901- 2000; 10 = 2001- 2201; and Fs = Family size
(1-5 persons in the home). Produce descriptive statistics for each variable and briefly discuss which statistics will be used to inform you about the normal distribution of your data. (10 marks)

Question 2 [45 Marks]

Read the fictitious scenario below and answer the question(s) which follow:

Table 2.1

Coding key:

• #TH= Hours spent in a training programme

• #HW= Number of hours worked per day
• #YE= Number of years employed
• #TH & #TW= Total training hours and hours worked
• #PP= Productivity output (units) of pool pumps

Use the data in Table 2.1 above and complete the below instructions:
(13 marks)

Required:

Run the regression in Excel to test whether a model containing the independent variables #TH & #HW; #TH; #HW and #YE significantly affects #PP. Show your results. Highlight the statistics of interest (6 marks)

Report on and interpret the summary output in 2.1.1 (7 marks)

Take the necessary steps in Excel to ‘fix the regression’ (multicollinearity) by removing the ‘superfluous’ variable(s). Show and interpret the result. (9 marks)

Conduct the appropriate multicollinearity diagnostic to test in Excel. Indicate which independent variables have the strongest correlation and which might produce multicollinearity in your model. Show and interpret your output.

Assume that you have decided to remove the variable #YE from the regression analysis model and only include variables #TH and #HW in the model. Run the appropriate regression analysis in Excel and show and report on the summary output. (10 marks)

Based on the elimination process followed in questions 2.1-2.5 you conclude that independent variable #TH and the dependent variable PP# are in a cause- effect relationship. Your H1 is that there is a cause-effect relationship between #TH and #PP. (6 marks)

Required:
Use the appropriate chart to confirm or refute whether the variables #TH and #PP is in a linear relationship. (1 mark)

Run the appropriate regression analysis in Excel to refute or confirm H1. Show your summary output. Highlight the statistics of interest. Report and interpret your results.

Question 3 [10 Marks]
Read the fictitious scenario below and answer the question which follows:

You are a market researcher for VUMA. VUMA has recently introduced a new home internet package. They now want to assess the uptake of this new internet package using a pilot study before conducting a large-scale survey. A random sample of 12 home internet users was selected from VUMA’s database and their monthly internet usage (in hours) was identified for March last year 2023 (period 1) and again in March (2024) (period 2). The data from this pilot study is shown below in Table 3.1

Table 3.1

Required:
Run the appropriate test in Excel for paired two sample for means. The assertion is that this new internet package will increase hours spent by subscribers on the internet. Show your summary output. Highlight the statistics of interest. Report on and interpret your summary output. (10 marks)

Question 4 [17 Marks]
Read fictitious scenario 4.1 below and answer the question(s) which follow.

Fictious scenario 4.1
The Global Entrepreneurship Monitor(GEM) is an international research group focusing on entrepreneurship across several countries, including South Africa. The research focuses on topics such as funding, entrepreneurial opportunities, and entrepreneurial mentoring. The researchers and subsequent publishers of the report, which is published bi-annually, wish to answer the following question: ‘Is the topic preferences of the readership of the GEM reports independent of gender? This is a critical concern for GEM given that there is a drive to increase female entrepreneurship in South Africa. A random selection of 200 burgeoning entrepreneurs (both male and female) was sourced from the Department of Small Business Development’s database of entrepreneurs and/or SMMEs. The sample profile shows that 80 females and 120 males were surveyed.
The results showed that:
• 46 respondents (13 females and 33 males) preferred reading topics on funding.
• 73 respondents (28 females and 45 males) preferred topics on entrepreneurial opportunities.
• 81 respondents( 39 females and 42 males) who preferred topics on entrepreneurial mentoring.

Required:
Produce a cross tabulation table of actual observations. (3 marks)
Produce a cross tabulation table of expected observations. (3 marks)

Run the CHISQ.TEST in Excel. Interpret the output statistic as a p-value in terms of the null and research hypotheses and report the Chi-Square test result in a format acceptable for dissertations and research reports. (5 marks)

Based on fictitious scenario 4.1 above, use the appropriate chart to present the percentage of male and female respondents for actual observation regarding their preferences for the topics (funding, entrepreneurial opportunities, and entrepreneurial mentoring) focused on in the bi-annual GEM reports. (6 marks)

Answers to Above Questions on Business Research Methods

Answer 1: The application of appropriate statistical technique to present a summary output and describe the characteristics of your dataset in Table 1.1.  is performed as follows:

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