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ASB2411 Quantitative methods for business: Assignment (20%)
The aim of this assignment is to demonstrate your ability to: • carry out basic calculations using MS Excel
• describe and summarise data using tables, graphs and measures of central tendency and dispersion
• estimate and specify confidence intervals • apply the methods of statistical inference to formulate and test hypotheses
• analyse data, and interpret the results
Task: In the spreadsheet file Country assignment_2017.xlsx (available on Blackboard), you have been assigned to study consumer price inflation in two countries, Country A and Country B. (The pair of countries assigned is different for each student). Annual Consumer Price Index (CPI) data for the period 1979-2010 for your two assigned countries can be extracted from the spreadsheet file cpi.xlsx. (The data in this file for all other countries should be ignored!)
1. Using the formula ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − π = − − t 1 t t 1 t p p p 100 , where πt is the annual percentage rate of inflation between years t–1 and t, and pt is the value of the CPI in year t, calculate πt for each year from t=1980 to t=2010 for Country A and for Country B. Using these data, complete the following table of descriptive statistics: Mean inflation Standard deviation of inflation Median inflation Minimum inflation Maximum inflation Country A 1980-1999 ? ? ? ? ? 2000-2010 ? ? ? ? ? Country B 1980-1999 ? ? ? ? ? 2000-2010 ? ? ? ? ? [Total – 25 marks] 2. Present time-series plots of inflation against time for: a. country A for the period 1980-2010. (5 marks) b. country B for the period 1980-2010. (5 marks) [Total – 10 marks]
3. Assuming that the annual inflation rates of Countries A and B are normally distributed, and interpreting each country’s data on πt for the period 1980-1999 as a random sample of 20 observations drawn from a fixed population distribution of all possible inflation rates for each country, construct the following confidence intervals, commenting briefly on what the confidence interval is demonstrating: a. 95% confidence interval for the population mean inflation rate of Country A. (5 marks) b. 99% confidence interval for the population mean inflation rate of Country A. (5 marks) c. 95% confidence interval for the population mean inflation rate of Country B. (5 marks) d. 90% confidence interval for the population mean inflation rate of Country B. (5 marks) [Total – 20 marks]
4. Assuming that the annual inflation rates of Countries A and B are normally distributed, and interpreting each country’s data on πt as a random sample, use appropriate hypothesis tests to evaluate the following assertions concerning the (population) mean inflation rates of Countries A and B. Use a significance level of α=0.05. Briefly comment on your answers.
a. Country A’s (population) mean inflation throughout the period 1980-2010 was 3%. (5 marks) b. Country B’s (population) mean inflation throughout the period 2000-2010 was less than 3.5%. (5 marks)
c. Country A’s (population) mean inflation during the 11-year period of euro membership 2000-2010 was significantly less than Country A’s (population) mean inflation during the 20-year period prior to euro membership 1980-1999. [Treat the observations on πt for the two periods as independent samples.] (5 marks) d. Country A’s (population) mean inflation during the period 2000-2010 was significantly different from Country B’s (population) mean inflation during the same period. [Treat the samples of observations on πt for the two countries during the period 2000-2010 as matched pairs.] (5 marks) [Total – 20 marks]
5. Country C, an applicant for EU membership, has an annual inflation rate that is known to behave as a normally distributed random variable, with a population mean and population variance identical to the numbers for the sample mean and sample variance reported for Country A during the period 2000-2010 (see Q1).
a. Calculate the probability that Country C’s inflation rate in any future year is less than 1.5%. (5 marks)
b. Calculate the probability that Country C’s inflation rate in any future year is greater than 2.5%. (5 marks)
c. Calculate the probability that Country C’s average inflation rate over the next 4 years is greater than 2%. (5 marks) [Total – 15 marks]
6. Using the data on πt in Country B for t=1980 to t=1999 (20 observations), calculate p = the proportion of years in which Country B’s rate of inflation was greater than 5%. In a certain emerging country D, which has an economic structure similar to that of Country B during the 1980s and 1990s, episodes of annual inflation above 5% are known to occur randomly, with a probability of p (as calculated above). The Governor of Country D’s central bank had set a maximum annual inflation target of 5% in each of the next 6 years.
a. Calculate the probability that Country D’s inflation target will not be breached in any of the next 6 years. (5 marks)
b. Calculate the probability that Country D’s inflation target will be breached in exactly 2 of the next 6 years. (5 marks) [Total – 10 marks] Guidance: Hints on how to go about answering questions 1 to 6 can be found in the Word file assignment_hints.doc (available on Blackboard) For Q1-Q2, only the completed table and graphs are required. It is not necessary to show the supporting calculations, and the spreadsheet file in which you have done the calculations is not required. For Q3-Q6, all solutions and supporting calculations are required. No marks will be awarded for solutions that refer to countries other than those you have been assigned personally (Please see ‘List of assigned countries’ on Blackboard for your assigned countries) Relevant lecture notes:
Part 1 – Presentation and description of data,
Part 2 – Probability Theory and