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Research Methods ASB 4601-Bangor Business School - Prifysgol Bangor University | 2018 Past paper solutions

Answer FOUR OF THE FIVE Questions

Question 1: THEORY (25 Marks)                                                             

• Explain the ANOVA method.
  Answer (Purchase past paper to get the full solution)
  Analysis of Variance or ANOVA is a statistical method used to compare two or more datasets by testing their differences of means. The inferences about means are made by analysing variances. This technique involves three key assumptions; independency of groups, normality in the distribution of each group and homogeneity of variances between the groups.

• Describe, in detail the steps followed for the ANOVA calculations and how those calculations result in the respective table.

Answer (Purchase past paper to get the full solution)

There are 7 steps involved in ANOVA calculations:

• First step is to define null and alternative hypothesis i.e.
Null hypothesis: H0: u1 = u2 = u3
Alternative hypothesis: Not all u’s are equal.

• Second step is to state the significance level (alpha value) for our test (usually given).

• Then we calculate the degrees of freedom for between treatments, within treatments
and total.
dF (between) = k – 1, dF (within) = N – k & dF (total) = N – 1
where k is the number of treatments or independent comparison groups and N is the total
number of observations or total sample size.

• State the critical value using two different degrees of freedom, dF (between) and dF
(within) and alpha value. Look for the critical value in F-table using these parameters
(dF (between), dF (within), alpha). This F value will be called F critical.

• Calculate the test statistic (F statistic). We need to have the sum of squares (SS) for
this first:
Sum of squares between (SSB), sum of squares within (SSW) and sum of squares (SST)
i.e.
where X is an individual observation, Xj is a sample mean of the jth treatment and X bar
is a overall sample mean.
Then we need to find mean squares (MS) by dividing each SS by the respective dF:
MSB = SSB/dF(between) MSW = SSW/dF(within)
Finally, the F statistic can be found as:
F = MSB/MSW

• State the results.

• State the conclusion. The decision rule will be if the F statistic will be greater than F
critical, reject the null hypothesis and the result is significant. Also, if the p-value is
less than the significance level, reject the null hypothesis and the result is significant.

• Draw an example of an ANOVA table and explain what is in each and every cell.
• Describe what the type of analysis ANOVA is useful for and why.

Answer (Purchase past paper to get the full solution)

The choice of ANOVA depends upon what we need to analyse in our research. There are 3
types of ANOVAs; one-way ANOVA, two-way ANOVA without replication and two-way
ANOVA with replication. One-way ANOVA is useful when you need to test two groups to
see the difference between them. Two-way ANOVA without replication is used when you
have one group and you are double testing that same group. Two-way ANOVA with
replication is used when you have two groups and the individuals of those groups are doing
more than one thing

• Explain any disadvantages in using the method.

Answer (Purchase past paper to get the full solution)

All the assumptions needs to be fulfilled before applying ANOVA. Also, if null hypothesis is
rejected, we know at least one group differs from others, but with a one-way ANOVA and
multiple groups, it may be difficult to determine which group is different

• Explain why and how it is used in the regression analysis.

Answer (Purchase past paper to get the full solution)

Analysis of Variance (ANOVA) consists of calculations that provide information about levels
of variability within a regression model and form a basis for tests of significance. The basic
regression line equation can be written as:
SST = SSM + SSE, where SS is sum of squares and T, M and E are total, model and error,
respectively. R-squared can be written as a ratio of SSM and SST i.e. r2 = SSM/SST.

• Describe the typical follow-up analysis undertaken after developing the ANOVA table.

                                                                                                           (25 marks)

Question : THEORY (50 Marks)                                                               

1. There are numerous ways in which sampling can be conducted for research. Describe three approaches to sampling and identify the strengths and weaknesses of each. (25 marks)
2. What is the difference between causality and correlation (25 marks)

Question 2: (25Marks)                                                                                                        

When we want to find a value representing the central location for a dataset we have more than one option and respective statistics to use, with the mean, the median and the mode being the most popular ones, but all these three come with some distinct advantages and disadvantages.

1. Discuss and highlight at least one of the advantages and one of the disadvantages for each of the mean, the median and the mode          (6 marks)
2. Give a numerical example of a dataset with at least 25 data points in order to illustrate the main disadvantage of the mean.                          (4 marks)                                              
3. Give a numerical example of a dataset with at least 25 data points in order to illustrate the main disadvantage of the mode.                          (4 marks)  
4. Draw two boxplots so as to compare the datasets you created in (ii) and (iii)                                                                                                                                                                              (6 marks)
5. Draw two Frequency polygons so as to compare the datasets you created in (ii) and (iii)                                                                                                                                                             (5 marks)

Question 3: (25 Marks)                                                                                                       

PharmaCo sells Medical Imaging Devices. PharmaCo  has just signed a contract to sell, on 02-Jul-2018, a batch of these expensive devices to various customers around the world. The following table shows the orders from seven customers.

The selling prices are fixed and in local currencies at the exchange rate prevailing at the time of the delivery – that is on 02-Jul-2018. Of course there is uncertainty in the exchange rates, and in order to cope with this uncertainty, estimates of the mean and the standard deviation of the exchange rates have been provided by the Bank of America for all but one (EUR) of the currencies. The report that came with these estimates stated that these rates are normally distributed and independent of one another. 

1. Find the distribution and report the mean and the standard deviation of the total revenue in $.                                                                            (10 marks)                                                                                   
2.   a) What is the probability that this revenue will exceed $ 2,290,000? (2 marks)                                                  b) What is the probability that this revenue will be less than $ 2,110,000? (2 marks)
3. HSBC offers to pay a sure sum of $2,150,000 (payment to be made on the 02 – Jul -2018) in return for the revenue in local currencies from the sales. Explain whether this a good offer for PharmaCo.  The CEO of PharmaCo is very risk-averse: explain whether you think he/she will accept the offer?                                                                                                                                                                                 (4 marks)                              
4. Explain why HSBC is making this offer and what is the probability that the bank will incur a loss? What other options does the bank have if they decide not to convert all/some of the currencies in to $ on 02 – Jul -2018? (4 marks)                                                                  
5. For the exchange rate of £/USD assume that estimates were not available. Describe a process for producing such estimates.                               (3 marks)

Question 4 (25 Marks)

The following data are the Years_of_Experience of the brokers in an investment firm, and the Annual_Return_Rates they achieve for whatever funds they control.

1. Plot the Annual_Return_Rates against Years_of_Experience and fit a straight line regression model to the data.                                                                           (6 marks)
2. Plot the residuals from the model against Years_of_Experience. What does this say about the fitted model?                                                                                  (4 marks)
3. What percentage of variation in Annual_Return_Rates is explained by the regression relationship?                                                                                                            (6 marks)
4. If we are about to hire a new trader with 33 years of experience, what would be the expected Annual_Return_Rates for him/her?                                               (4 marks)
5. Explain why the result in (IV) is not exactly 10 as prescribed from the real data             (5 marks)

Question 5 (25 Marks)

The following Stata output refers to a regression for the determinants of the return on assets for a sample of 100 banks in a particular year. The variable definitions are as follows:

roa = percentage return on assets

lasset = natural logarithm of asset value (expressed in £ billions)

list = 1 if the bank is stock market-listed, 2 otherwise.

Required

I  Interpret the following from the Stata output:

• Coefficients on lasset and list, and their t-statistics and p-values.   (4 marks)
• R-squared                                                                                  (2 marks)
• The F-statistic                                                                          (2 marks)
• The Adj R-squared                                                                   (2 marks)
• Explain why we use, as a variable, 'lasset' and not just 'asset'?  (5 marks)

II   What is the expected return on assets for a non-listed bank with an asset value of £30 billion?                (10 marks)

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Last updated: Sep 27, 2019 05:37 AM