Question 2 (20 marks) The Australian Bureau of Statistics regularly reports on large percentages of small businesses failing. In a bid to identify potential indicators, or symptoms, of business failure, a national study of small businesses was undertaken. A random sample of 85 small businesses was obtained and characteristics measured. One of the recorded variables was the ratio of current assets to current liabilities (variable name Asset_Liability_Ratio); roughly speaking, this is the amount that the firm is worth divided by what it owes. Five years later these same small businesses were revisited. Among the variables collected was whether the small business was still operating or not; the latter meaning the business had failed or closed (variable name Operational). This is an example of what is known as a longitudinal study The study was interested in, amongst many measures of performance, assessing whether the previously-recorded ratio of current assets to liabilities differed between small businesses which were still operating five years later and those that were not The data is provided in the file Question2.xls: Columns A and contain the two variables, Columns D and E contain the same data organised differently. a) One key variable represents the ratio of current assets to liabilities at the time of the original study (abbreviated hereafter to Asset Liability Ratio). The second key variable represents whether or not the small business is still operational (abbreviated hereafter to Operational and having the values Yes and No to indicate still operational or now-closed respectively). Identify each variable's type as either Continuous, Discrete, Ordinal or Nominal. [2 marks] b) Use Excel to construct a histogram of Asset Liability Ratio for all 85 small businesses. How would you describe the shape? Include your histogram after finding a suitable number of bins. [2 marks] c) Which graphical presentation would be useful to compare the Asset Liability Ratio for the now-closed and still operational small businesses? Name and provide the visual display using Excel. [2 marks] d) Use Excel to find the mean, median, standard deviation and interquartile ranges of the Asset Liability Ratio for the now-closed small businesses. Repeat for the still operational small businesses. Do not simply include raw output. [2 marks] e) Using your output created in parts b) - d), give a brief report comparing the Asset Liability Ratio for the now-closed and still operational small businesses. [4 marks] f) An economist suggested that small businesses that were still operational would most likely have had an Asset Liability Ratio above 1.97 (five years previous). 1. Use the empirical rule to (approximately) estimate the probability of a small business which is still operational having had an Asset Liability Ratio above 1.97 (five years previous). Show your working. Do NOT use the computer to get a more accurate answer. NOTE: round the mean and standard deviation you obtained earlier to 2 decimal places before using them to estimate the probability via the empirical rule. 2. Does it appear the economist's claim is well-supported by the study? Explain. [2 marks] g) Prior to the above analysis, the same economist had commented that based on her experience she expected a difference in mean Asset Liability Ratio, for small businesses which were still operating five years later and those that were not, of at least 1. Explain, using support from a hypothesis test performed at the 5% significance level, what you would conclude about this comment. [6 marks] Question 2 (20 marks) The Australian Bureau of Statistics regularly reports on large percentages of small businesses failing. In a bid to identify potential indicators, or symptoms, of business failure, a national study of small businesses was undertaken. A random sample of 85 small businesses was obtained and characteristics measured. One of the recorded variables was the ratio of current assets to current liabilities (variable name Asset_Liability_Ratio); roughly speaking, this is the amount that the firm is worth divided by what it owes. Five years later these same small businesses were revisited. Among the variables collected was whether the small business was still operating or not; the latter meaning the business had failed or closed (variable name Operational). This is an example of what is known as a longitudinal study The study was interested in, amongst many measures of performance, assessing whether the previously-recorded ratio of current assets to liabilities differed between small businesses which were still operating five years later and those that were not The data is provided in the file Question2.xls: Columns A and contain the two variables, Columns D and E contain the same data organised differently. a) One key variable represents the ratio of current assets to liabilities at the time of the original study (abbreviated hereafter to Asset Liability Ratio). The second key variable represents whether or not the small business is still operational (abbreviated hereafter to Operational and having the values Yes and No to indicate still operational or now-closed respectively). Identify each variable's type as either Continuous, Discrete, Ordinal or Nominal. [2 marks] b) Use Excel to construct a histogram of Asset Liability Ratio for all 85 small businesses. How would you describe the shape? Include your histogram after finding a suitable number of bins. [2 marks] c) Which graphical presentation would be useful to compare the Asset Liability Ratio for the now-closed and still operational small businesses? Name and provide the visual display using Excel. [2 marks] d) Use Excel to find the mean, median, standard deviation and interquartile ranges of the Asset Liability Ratio for the now-closed small businesses. Repeat for the still operational small businesses. Do not simply include raw output. [2 marks] e) Using your output created in parts b) - d), give a brief report comparing the Asset Liability Ratio for the now-closed and still operational small businesses. [4 marks] f) An economist suggested that small businesses that were still operational would most likely have had an Asset Liability Ratio above 1.97 (five years previous). 1. Use the empirical rule to (approximately) estimate the probability of a small business which is still operational having had an Asset Liability Ratio above 1.97 (five years previous). Show your working. Do NOT use the computer to get a more accurate answer. NOTE: round the mean and standard deviation you obtained earlier to 2 decimal places before using them to estimate the probability via the empirical rule. 2. Does it appear the economist's claim is well-supported by the study? Explain. [2 marks] g) Prior to the above analysis, the same economist had commented that based on her experience she expected a difference in mean Asset Liability Ratio, for small businesses which were still operating five years later and those that were not, of at least 1. Explain, using support from a hypothesis test performed at the 5% significance level, what you would conclude about this comment. [6 marks]