Question 1:
Compare monthly number of pledges received between pre-Year 2000 and post-Year 2000. Use descriptive statistics to describe and interpret the data on number of pledges received. You are required to identify the measures of location and dispersion as well as organise the appropriate output from your software into a relevant statistical and graphical presentation of the data. Justify your choices. What are your preliminary observation/s?
Hint: Summaries and presentations should help you decide subsequent analysis.
Question 2:
(a) Identify the probability of the sample mean of number of pledges (monthly) received post-Year 2000 is more than 260,000 per month. Assume that the standard deviation for number of pledges received can be approximated by the sample standard deviation.
(b) Construct and state the 90% confidence intervals for the amount of loans (monthly) given out for the period pre-Year 2000 and post-Year 2000. Interpret these confidence intervals in your report. With these findings, can you validate if the amount of loans given out during those two periods is different?
(c) List the key assumption(s) you have made in constructing this confidence interval. Discuss if this/these assumption(s) is (are) reasonable.
(d) Explain what will be your follow-up actions including statistical tests, if the key assumption(s) were found to be violated.
Question 3:
Mr Owen Shaw claims that the hearsay from business associate is that since 2008-2009 crisis, the pawn broking business has not improved much in terms of loans redemption with interest (high volume of loans redemption with interests represents more profit for the pawn brokers).
Select an appropriate test of hypothesis to determine if the mean amount of loans redeemed, including interest, has increased significantly between pre-financial crisis (2000 - 2009) and post-financial crisis (2010 onwards).
You should include the following:
(a) State the null and alternative hypotheses and explain how you developed these two hypotheses.
(b) Use the output from your software for an appropriate hypothesis test with α = 0.05. List the test statistic you will use for this test. Explain your decision criteria.
(c) Discuss the assumptions you have made in performing the hypothesis test. Are these assumptions reasonable for this case? Please provide explanation/s to substantiate your view.
Question 4:
Interpret the above statistical testing outcome and highlight three (3) possible business or statistical concerns regarding the approach used here in determining whether the mean amount of loans redeemed including interest has significantly improved post-financial crisis.
If your group has a free hand on the project, starting from measurements, sampling, to analysis, what recommendations would you give for the problem in question?
Keep your answer within 400 to 500 words (indicate your word count)
Question 5:
In about 300 words (indicate your word count), provide an executive summary of your analysis and findings to Mr. Owen Shaw with respect to pawn broking operations in Singapore and business prospects.