2. Empowerdem is a not-for-profit organisation that provides capacity building support to Micro, Small and Medium-sized Enterprises (MSMEs) across the Southern Africa Development Community (SADC). Empowerdem’s mission is to build the capacity of MSMEs in order to contribute to economic growth and prosperity, increase resilience and stimulate job creation. Due to increased demand for its services, Empowerdem is contemplating a strategic shift with the aim of prioritising the provision of evidence-driven support for MSMEs. The operations director, Mr Kelvin Africa, is spearheading Empowerdem’s operational plan which is premised on sharpening entrepreneurial behaviours that predict business performance across the SADC region.
He believes that building the capacity of MSMEs and nudging firms in the MSME space towards better business practices is important for improved business performance and enhanced contribution to economic growth across SADC. In this regard, he has hypothesised that entrepreneurial orientations of MSMEs correlate with business performance. Mr Simon Mokwena, a business analyst at Empowerdem, has been tasked with conducting an analysis of entrepreneurial orientations and business performance of MSMEs across five (5) SADC countries, namely South Africa, Namibia, DR Congo, Zimbabwe and Tanzania. He carried out a hypothesis testing and the result yielded a p-value of 0.0025. Explain in detail the steps of the hypothesis testing and draw your conclusion. (10 marks)
3. A box contains 10 balls out of which 2 are green, 5 are red and 3 are black. If two balls are drawn at random, one after the other without replacement, from the box. Find the probabilities that:
(a) both the balls are of green color (b) both the balls are of black color
(c) both the balls are of red color
(d) the first ball is red and the second one is black
(e) the first ball is green and the second one is red (10 marks)
4. A study was conducted to determine urine flow of sheep (in milliliters/minute) when infused intravenously with an antidiuretic hormone ADH. The urine flows of 10 sheep are recorded as follows. 0.7 0.5 0.5 0.6 0.5 0.4 0.3 0.9 1.2 0.9 a. Determine the mean, the median, the mode and the quartiles for these sample data.
b. Suppose that the largest measurement is 6.8 rather than 1.2. How does this affect the mean, the median, and the mode?
c. Compute the range and the sample standard deviation.
d. How are the range and standard deviation affected, if the largest measurement is 6.8 rather than 1.2? e. Compute the coefficient of variation.
f. Discuss when is the coefficient of variation a better measure of dispersion than the standard deviation
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