Subject: QUANTITATIVE TECHNIQUES IN BUSINESS (QTB)

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PSAF – May 2018 – L2 – Q5 – The Budgeting Process in the Public Sector

Explains the concept of a national budget, surplus and deficit budget implications, and challenges in the implementation of national budgets in Nigeria.

Question

In government’s quest to optimally develop and efficiently manage available resources, national budgets are usually prepared to put economic development firmly on course.

Required:

a. Describe briefly a national budget. (3 Marks)

b. Explain briefly the implication of each of the following for the performance of the economy: i. A surplus budget ii. A deficit budget (4 Marks)

c. Explain FOUR problems to be encountered in the effective implementation of national budgets in Nigeria. (8 Marks)

Answer

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Tags: Budget Implementation, Deficit Budget, National Budget, Surplus Budget
Level: Level 2

Topic: Budgeting
Series: MAY 2018

QTB – Nov 2014 – L1 – SB – Q6 – Mathematics of Business Finance

Calculate the value of an investment with compound interest, the payoff amount for a loan with simple interest, and the additional interest for a loan with monthly payments and reduced interest rates.

Question

a. If N250,000 is invested in an account that earns 4% per year compound interest, what is the:
i. value of the investment after 5 years? (3 Marks)
ii. total interest earned? (2 Marks)

b. When it was apparent that your parents could not afford to finance your university education, you sought and obtained a 4-year loan of N250,000.00 from Education Bank Limited. The bank imposed a simple interest rate of 7½%.
i. How much do you need to pay off the bank now

(4 years after) that you are through with your study?

(7 Marks)
ii. If you decide to be paying N25,000 every month from now and the bank agreed to reduce the interest rate to 1% per month on the unpaid balance at the beginning of the month, how much additional total interest will be paid? (8 Marks)

Answer

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Tags: Compound Interest, Interest calculation, Loan Repayment, Simple Interest
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

QTB – Nov 2014 – L1 – SB – Q5b – Data Collection Analysis

Draw a frequency polygon and an ogive based on gasoline mileage data from an experiment.

Question

In a particular organisation, an experiment which was conducted to determine the gasoline mileage of a particular type of car yielded the following data:

Miles per gallon	Percent
10 and under 12	4
13 and under 15	8
16 and under 18	14
19 and under 21	26
22 and under 24	12
25 and under 27	11
28 and under 30	10
31 and under 33	7
34 and under 36	6
37 and under 39	2

Required:

i. Draw the frequency polygon for gasoline mileage. (5 Marks)
ii. Draw the ogive for gasoline mileage. (5 Marks)

Answer

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Tags: Frequency Polygon, Gasoline Mileage, Graphical Representation, Ogive
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2014

QTB – Nov 2014 – L1 – SB – Q5a – Statistics

Calculate the Spearman's rank correlation coefficient between the scores in two subjects and interpret the result.

Question

A business school preparing candidates for professional examinations conducted a mock examination to ascertain the level of preparedness of its candidates in two subjects: Quantitative Techniques in Business (QTB) and Management Information (MI). The table below gives the scores of twelve selected candidates.

Candidates	1	2	3	4	5	6	7	8	9	10	11	12
Score in QTB (x)	35	77	95	28	76	80	90	62	39	65	90	37
Score in MI (y)	50	82	89	58	65	61	84	59	48	53	80	52

Required:
i. Calculate the Spearman’s rank correlation coefficient between $x$ and $y$ . (9 Marks)
ii. Comment on the result in (i) above. (1 Mark)

Answer

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Tags: Correlation, Mock Examination Scores, Spearman’s Rank
Level: Level 1

Topic: Statistics
Series: NOV 2014

QTB – Nov 2014 – L1 – SB – Q4 – Forecasting

Analyze sales data using the Least Squares Method and forecast future sales based on the trend.

Question

The sales of PQR Nigeria Plc. in thousands of Naira are listed in the table below for each quarter for years 2005 – 2008.

Sales of PQR in N’000s

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
2005	22	35	82	37
2006	24	46	81	44
2007	25	40	87	49
2008	29	42	100	55

Required:

a. Calculate the trend in the above data using the Least Squares Method. (12 Marks)
b. Estimate the sales for each quarter using the trend line. (4 Marks)
c. Calculate the percentage variation for each quarter’s actual sales from the estimate obtained in (b) above. (4 Marks)

(Total: 20 Marks)

Answer

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Tags: Least Squares, Sales Forecasting, Time series, Trend Estimation
Level: Level 1

Topic: Forecasting
Series: NOV 2014

QTB – Nov 2014 – L1 – SB – Q3 – Operations Research

Calculate control levels for inventory, expected time for a project, and identify the critical path in a network diagram.

Question

a. Calculate the various control levels from the following data on a given inventory item:

Normal usage: 1,600 per day
Minimum usage: 1,000 per day
Maximum usage: 3,000 per day
Lead time: 16 – 20 days
EOQ: 40,000
(9 Marks)

b. If the optimistic, most likely, and pessimistic times are given as 11 days, 15 days, and 18 days respectively, calculate the expected time of the project delivery.
(3 Marks)

c. The network for a small building project is shown below together with the time in days required to complete each task.

Required:

i. List the possible paths together with their durations through the network. (6 Marks)
ii. State the critical path and the project duration. (2 Marks)

(Total: 20 Marks)

Answer

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Tags: Control Levels, Critical Path, Economic Order Quantity (EOQ), Expected Time, Network Analysis
Level: Level 1

Topic: Operations Research
Series: NOV 2014

QTB – Nov 2014 – L1 – SB – Q2 – Measures of Dispersion

Compare the risk and return of two investments by calculating mean and standard deviation.

Question

In finance, the standard deviation is frequently used to measure the risk of an investment.
An investor is considering two possible investments A and B. A sample of 10 rates of return is recorded for each investment. These rates of return, given as percentages, are as follows:

Investment A:
4, 6, 6, 5, 4, 5, 8, 5, 5, 8

Investment B:
0, -2, 6, 12, 9, 16, -4, 16, 25, 12

Required:
a. Calculate the mean rate of return for each of the two investments. (6 Marks)
b. Calculate the standard deviation of the rate of return for each of the investments. (6 Marks)
c. Which of the two investments is riskier and why? (8 Marks)

(Total: 20 Marks)

Answer

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Tags: Investment Analysis, Mean, Risk Assessment, Standard Deviation
Level: Level 1

Topic: Measures of Dispersion
Series: NOV 2014

QTB – Nov 2014 – L1 – SB – Q1b – Mathematics of Business Finance

Determine the total sum of money the Chief Accountant of Zeesco Plc. plans to donate to 4 not-for-profit organisations, given the donations for each organisation.

Question

The Chief Accountant of Zeesco Plc. has a large sum of money which she plans to donate to 4 not-for-profit organisations. She plans to give of this amount to organisation A. Out of the remaining amount, she plans to give to organisation B. Also, she intends to give of the balance to organisation C and the rest to organisation D. If she plans to give 11 million naira to organisation D, how much does she plan to share among these organisations?

Answer

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Tags: Algebraic Fractions, Charity Donations, Fractions, Proportional Distribution
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

QTB – May 2017 – L1 – SB – Q6b – Data Collection Analysis

Calculate the mode and Pearson's coefficient of skewness for a given distribution of marks.

Question

The table below shows the marks (%) scored in QTB by some candidates who wrote the ICAN Professional examination in May 2016 diet:

Marks %	Number of Candidates
20–29	7
30–39	17
40–49	13
50–59	9
60–69	4

If the mean mark is 41.7%, calculate the mode and Pearson’s coefficient of skewness. (10 Marks)

Answer

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Tags: Mode, Pearson’s Coefficient, Skewness
Level: Level 1

Topic: Data Collection
Series: MAY 2017

QTB – Nov 2014 – L1 – SB – Q1a – Mathematics of Business Finance

Determine the cost of calculators and books using a system of linear equations and solve for individual costs.

Question

The cost of purchasing 8 calculators and 10 books is 158 (thousands of naira).
At another instance, the cost of purchasing 15 calculators and 3 books is 123 (thousands of naira).

Required:
i. Use the information above to write down a system of linear equations to describe the given cost scenario. (4 Marks)
ii. Solve the resulting system of equations. (4 Marks)
iii. Find the cost of each calculator and each book. (2 Marks)

Answer

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Tags: Cost Calculation, Linear Equations, Simultaneous Equations
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2014

QTB – May 2016 – L1 – SA – Q20 – Operations Research

Calculating traffic intensity or utilization factor in a simple queue given arrival and service rates.

Question

In a simple queue, if the arrival rate is 5 customers in 15 minutes and the service rate is 8 customers in 12 minutes. the traffic intensity or utilization factor is

A. 0.25
B. 0.50
C. 0.55
D. 0.65
E. 1.00

Answer

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Tags: Arrival Rate, Queuing Theory, Service Rate, Traffic Intensity
Level: Level 1

Topic: Operations Research
Series: MAY 2016

QTB – May 2016 – L1 – SA – Q19 – Operations Research

Expressing a production time constraint for two products given limited direct labour hours.

Question

A company makes two products X and Y. It takes 2¼ hours to make one unit of X and 3¾ hours to make one unit of Y. If only 18,000 direct labour hours are available, then the production time constraint is expressed as

A. 3.75x + 2.25y ≤ 18,000
B. 2.25x + 3.75y ≤ 18,000
C. 3.75x + 2.25y ≥ 18,000
D. 2.75x + 3.75y ≥ 18,000
E. 3.75x + 2.25y = 18,000

Answer

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Tags: Linear Programming, Production Constraints, Time Management
Level: Level 1

Topic: Operations Research
Series: MAY 2016

QTB – May 2016 – L1 – SA – Q18 – Statistics

Calculating the probability of total sales of 6 in two consecutive days given daily sales probabilities.

Question

The daily sales record of a company with their corresponding probabilities are tabulated as follows:

The probability of total sales of 6 in two consecutive days is

A. 0.1039
B. 0.1309
C. 0.1930
D. 0.3019
E. 0.3109

Answer

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Tags: Compound Events, Probability, Sales Forecasting
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – May 2016 – L1 – SA – Q17 – Statistics

Calculating the trend stock for a future month based on historical stock figures.

Question

A company takes stock for 5 months in each year. The stock figures of materials for the most recent three years are as tabulated below:

Determine the trend stock for month 6.

A. 84

B. 85

C. 86

D. 87

E. 88

Answer

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Tags: Forecasting, Time series, Trend Analysis
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – Nov 2015 – L1 – SB – Q5b – Statistics

Calculate Pearson’s correlation coefficient between company expenditure and income over eight years and interpret the result.

Question

An auditing firm is carrying out an analytical review of the financial transactions of its client, XYZ Manufacturing Company Limited. In order to ascertain the relationship that exists between the company’s annual expenditure and annual income, the following information was extracted from the company’s record for eight different years:

Years	1	2	3	4	5	6	7	8
Expenditure (x)	30	25	40	35	50	30	55	20
Income (y)	42	45	55	50	60	40	70	35

You are required to:

i. Calculate the Pearson’s product-moment correlation coefficient between $x$ and $y$ . (9 Marks)

ii. Comment on the result in (i). (1 Mark)

(Total: 10 Marks)

Answer

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Tags: Data Relationship, Expenditure, Financial Analysis, Income, Pearson Correlation
Level: Level 1

Topic: Statistics
Series: NOV 2015

QTB – MAY 2016 – L1 – SA – Q16 – Statistics

Identify the statistical measure used to determine the degree of association between variables

Question

Which of the following is used to measure the degree of association between two variables?

A. Regression

B. Percentiles

C. Quartiles

D. Correlation E. Coefficient of variation

Answer

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Tags: Correlation, Regression, Statistical Analysis
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – Nov 2015 – L1 – SB – Q5a – Data Collection Analysis

Calculate the mean, median, and mode for the given distribution of student scores.

Question

A group of 24 final year students participated in an Economic Theory Test and their scores were recorded as follows:

12, 14, 18, 7, 11, 15,
8, 15, 10, 14, 19, 9,
14, 6, 13, 14, 12, 16,
10, 9, 12, 15, 8, 17

Required:

Determine the:

Mean,
Median, and
Mode of this distribution.

(Total: 10 Marks)

Answer

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Tags: Data Analysis, Mean, Median, Mode, Student Scores
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2015

QTB – MAY 2016 – L1 – SA – Q15 – Statistics

Identify the graph used to plot a Time Series

Question

The plot of a Time Series as a graph is called

A. Histogram
B. Ogive
C. Pie chart
D. Historigram
E. Z-chart

Answer

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Tags: Data Visualization, Time Series Analysis
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – Nov 2015 – L1 – SB – Q4 – Statistics

Calculate probabilities related to defective items using a tree diagram for a production company with three lines.

Question

A production company has three production lines $L_1$ , $L_2$ , and $L_3$ .

The table below shows the percentage of items produced and percentage of defective items from each line:

Production Line	Percentage Produced (%)	Percentage Defective (%)
$L_1$	35	4
$L_2$	25	2
$L_3$	40	3

You are required to:

a. Draw the tree diagram for the production company. (7 Marks)

b. Use your tree diagram to obtain the probability that:

The company produces defective items. (8 Marks)
If there is a defective item from the company, it is either from $L_1$ or $L_3$ . (5 Marks)

(Total: 20 Marks)

Answer

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Tags: Defective Items, Probability, Production Lines, Tree Diagram
Level: Level 1

Topic: Statistics
Series: NOV 2015

QTB – Nov 2015 – L1 – SB – Q3 – Data Collection Analysis

Calculate the semi-interquartile range and standard deviation for the income distribution of families.

Question

The table below shows the hypothetical incomes of some families in a locality:

Income (N)	Percent (%)
1000 – 1999	6.2
2000 – 2999	5.9
3000 – 3999	7.2
4000 – 4999	8.8
5000 – 5999	7.8
6000 – 6999	15.0
7000 – 7999	17.6
8000 – 8999	12.8
9000 – 9999	8.5
10,000 – 10,999	10.2

Required:

a. Determine the semi-interquartile range for the incomes of the families. (10 Marks)

b. Determine the standard deviation for the incomes of the families. (10 Marks)

(Total: 20 Marks)

Answer

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Tags: Data Analysis, Income Distribution, Semi-Interquartile Range, Standard Deviation
Level: Level 1

Topic: Data Collection Analysis
Series: NOV 2015

Subject: QUANTITATIVE TECHNIQUES IN BUSINESS (QTB)

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PSAF – May 2018 – L2 – Q5 – The Budgeting Process in the Public Sector

Explains the concept of a national budget, surplus and deficit budget implications, and challenges in the implementation of national budgets in Nigeria.

You're reporting an error for "PSAF – May 2018 – L2 – Q5 – The Budgeting Process in the Public Sector"

QTB – Nov 2014 – L1 – SB – Q6 – Mathematics of Business Finance

Calculate the value of an investment with compound interest, the payoff amount for a loan with simple interest, and the additional interest for a loan with monthly payments and reduced interest rates.

You're reporting an error for "QTB – Nov 2014 – L1 – SB – Q6 – Mathematics of Business Finance"

QTB – Nov 2014 – L1 – SB – Q5b – Data Collection Analysis

Draw a frequency polygon and an ogive based on gasoline mileage data from an experiment.

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QTB – Nov 2014 – L1 – SB – Q5a – Statistics

Calculate the Spearman's rank correlation coefficient between the scores in two subjects and interpret the result.

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QTB – Nov 2014 – L1 – SB – Q4 – Forecasting

Analyze sales data using the Least Squares Method and forecast future sales based on the trend.

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QTB – Nov 2014 – L1 – SB – Q3 – Operations Research

Calculate control levels for inventory, expected time for a project, and identify the critical path in a network diagram.

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QTB – Nov 2014 – L1 – SB – Q2 – Measures of Dispersion

Compare the risk and return of two investments by calculating mean and standard deviation.

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QTB – Nov 2014 – L1 – SB – Q1b – Mathematics of Business Finance

Determine the total sum of money the Chief Accountant of Zeesco Plc. plans to donate to 4 not-for-profit organisations, given the donations for each organisation.

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QTB – May 2017 – L1 – SB – Q6b – Data Collection Analysis

Calculate the mode and Pearson's coefficient of skewness for a given distribution of marks.

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QTB – Nov 2014 – L1 – SB – Q1a – Mathematics of Business Finance

Determine the cost of calculators and books using a system of linear equations and solve for individual costs.

You're reporting an error for "QTB – Nov 2014 – L1 – SB – Q1a – Mathematics of Business Finance"

QTB – May 2016 – L1 – SA – Q20 – Operations Research

Calculating traffic intensity or utilization factor in a simple queue given arrival and service rates.

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QTB – May 2016 – L1 – SA – Q19 – Operations Research

Expressing a production time constraint for two products given limited direct labour hours.

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QTB – May 2016 – L1 – SA – Q18 – Statistics

Calculating the probability of total sales of 6 in two consecutive days given daily sales probabilities.

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QTB – May 2016 – L1 – SA – Q17 – Statistics

Calculating the trend stock for a future month based on historical stock figures.

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QTB – Nov 2015 – L1 – SB – Q5b – Statistics

Calculate Pearson’s correlation coefficient between company expenditure and income over eight years and interpret the result.

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QTB – MAY 2016 – L1 – SA – Q16 – Statistics

Identify the statistical measure used to determine the degree of association between variables

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QTB – Nov 2015 – L1 – SB – Q5a – Data Collection Analysis

Calculate the mean, median, and mode for the given distribution of student scores.

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QTB – MAY 2016 – L1 – SA – Q15 – Statistics

Identify the graph used to plot a Time Series

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QTB – Nov 2015 – L1 – SB – Q4 – Statistics

Calculate probabilities related to defective items using a tree diagram for a production company with three lines.

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QTB – Nov 2015 – L1 – SB – Q3 – Data Collection Analysis

Calculate the semi-interquartile range and standard deviation for the income distribution of families.

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