Posted: February 3rd, 2015

Quantitative Methods for Business

Paper, Order, or Assignment Requirements

 

ASB-2411             Quantitative Methods for Business

 

Coursework assignment

 

In the spreadsheet file list.xlsx, 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). Hints on how to go about answering questions 1 to 6 below can be found in the Word file assignment_hints.doc.

 

1. Using the formula , where pt 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 pt 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:

(i)            country A for the period 1980-2010. (5 marks)

(ii)           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 pt 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:

 

(i)            95% confidence interval for the population mean inflation rate of Country A. (5 marks)

(ii)           99% confidence interval for the population mean inflation rate of Country A. (5 marks)

(iii)          95% confidence interval for the population mean inflation rate of Country B. (5 marks)

(iv)         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 pt 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:

 

(i)            Country A’s (population) mean inflation throughout the period 1980-2010 was

3%. (5 marks)

(ii)           Country B’s (population) mean inflation throughout the period 2000-2010 was

less than 3.5%. (5 marks)

(iii)          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 pt for the two periods as independent samples.]

(5 marks)

(iv)         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 pt 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).

 

(i)            Calculate the probability that Country C’s inflation rate in any future year is

less than 1.5%. (5 marks)

(ii)           Calculate the probability that Country C’s inflation rate in any future year is

greater than 2.5%. (5 marks)

(iii)          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 pt 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.

 

(i)            Calculate the probability that Country D’s inflation target will not be breached

in any of the next 6 years. (5 marks)

(ii)           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]

 

Submission requirements: Submission of the hard-copy of a report containing the solutions to Q1-Q6 is required. The hard copy should be submitted at the College Administrative Centre. Turnitin submission of an electronic copy of this report is not required.

 

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. These may be either typed or (legibly) hand-written.

 

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)

 

Submission deadline:     Tuesday 16th December, 3pm.