Topic: Statistics

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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.

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 – May 2017 – L1 – SB – Q6a – Statistics

Calculate the monthly cost of replacing diodes based on failure probability and determine if a student can buy a gown based on expected money.

Question

i. The laptops that are purchased by a company have 742 diodes with a life span of five months. These diodes fail on a regular basis according to the following probability distribution:

Life (months)	1	2	3	4	5
Probability of failure	0.10	0.30	0.35	0.20	0.05

If the cost of replacing a diode is ₦100, calculate the monthly cost of replacing the diodes as they fail. (4 Marks)

ii. Tadet, a student in the Accountancy Department of a Polytechnic, has the following chances of receiving money from her relatives:

45% chance of receiving ₦5,000 from her sister,
33% chance of receiving ₦8,000 from her brother,
16% chance of receiving ₦11,000 from her aunt,
6% chance of receiving ₦15,000 from her uncle.

Determine if Tadet will be able to buy a gown worth ₦8,000 from the money she is expecting from her relatives. (6 Marks)

Answer

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Tags: Cost Calculation, Expected Value, Financial planning, Probability Distribution
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SB – Q5b – Statistics

Calculate the Spearman's rank correlation coefficient between two accountants' rankings of ten banks.

Question

Two Chartered Accountants: X and Y, were requested to rank ten banks A, B, C, D, E, F, G, H, I, J according to their performances during a financial year. X ranked the banks as follows:

X’s Rankings: E, B, G, A, C, D, H, F, J, I
Y’s Rankings: E, C, A, B, G, H, J, D, F, I

Calculate the Spearman’s rank correlation coefficient between X and Y and interpret your result.

Answer

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Tags: Rank Correlation, Spearman's Coefficient\
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SB – Q4a – Statistics

Calculate the proportion of damaged blocks and the probability of taking a damaged block from a specific lorry using a tree diagram.

Question

a. A fleet of lorries A, B, and C are loaded with blocks meant for a building site.
Lorry A carries of all the needed blocks, B carries of what lorry A carries, and lorry C carries the rest. Lorries A, B, and C contain 13%, 15%, and 11% damaged blocks, respectively.

By drawing a suitable tree diagram, calculate:
i. The proportion of damaged blocks in the fleet. (8 Marks)

ii. The probability of randomly taking a damaged block from lorry B. (2 Marks)

Answer

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Tags: Damaged Blocks, Probability, Tree Diagram
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SB – Q2a – Statistics

Probability calculations for dice roll and random sampling in block production.

Question

i. A six-sided and fair die is thrown into the air. What is the probability:

Of NOT getting a SIX?
That either a THREE, a FOUR, or a FIVE will fall uppermost?
Of obtaining an even number?
(5 Marks)

ii. A block-making factory produces TWO types of blocks: 6-inch and 9-inch. ONE quarter of its output on a particular day are 6-inch blocks, while the remaining three-quarters are 9-inch blocks. If samples of 3 are taken at random, what is the probability of obtaining:

One 6-inch block?
Two 6-inch blocks?
One or two 6-inch blocks?
(5 Marks)

Answer

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Tags: Block Manufacturing, Dice, Probability, Sampling
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q18 – Statistics

This question calculates the centered moving average for a specific year in a time series of cocoa production.

Question

A ten-year record of cocoa production in a certain farm is tabulated as follows:

Year	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012
Production (tonnes)	42	52	41	48	64	67	77	66	73	89

Based on a 4-year moving total, the centered moving average for the year 2007 is:
A. 79.5
B. 69.5
C. 59.5
D. 49.5
E. 39.5

Answer

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Tags: Business Statistics, Moving Average, Time series
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q17 – Statistics

This question checks the range of values for the correlation coefficient r.

Question

If $r$ is the correlation coefficient calculated for a bivariate data, then which one of the following is correct?

A. $1$
B.
C.
D.
E.

Answer

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Tags: Bivariate Data, Business Statistics, Correlation
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q16 – Statistics

This question asks to identify a false statement about normal distribution.

Question

Which of the following is NOT TRUE about Normal Distribution?
A. Normal distribution is a frequency distribution.
B. Both tails of the distribution approach but never meet the horizontal axis.
C. It is a probability distribution of a continuous variable that fits many naturally occurring distributions.
D. The exact shape of the normal curve depends on the mean of the distribution.
E. The area under the normal curve represents the probability and totals 1 or 100%.

Answer

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Tags: Business Statistics, Normal distribution, Probability
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q15 – Statistics

This question involves calculating the probability that a defective item is from process B.

Question

A large batch of components of TV sets is stocked by a company. The batch comprises components that are manufactured by processes A, B, and C. There are twice as many components from process A as from each of processes B and C in a batch. Components from A contain 8% defectives, and those from B and C contain 11% and 14% defectives respectively.
The probability that a defective item is from process B is:
A. 0.228
B. 0.238
C. 0.248
D. 0.258
E. 0.268

Answer

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Tags: Business Mathematics, Defective Items, Probability
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q14 – Statistics

This question involves identifying the estimable components of a time series.

Question

The TWO components of a Time Series which are usually estimable are:
A. Trend and Cyclic variation
B. Seasonal variation and Trend
C. Random movements and Trend
D. Seasonal variation and Random movements
E. Cyclic variation and Seasonal variation

Answer

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Tags: Forecasting, Seasonal Variation, Time series, Trend
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q13 – Statistics

This question calculates the probability of rolling either a four or a six on a six-sided die.

Question

A six-sided die is thrown into the air, the probability that either a FOUR or a SIX will fall upper most is:

Answer

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Tags: Business Mathematics, Dice, Probability
Level: Level 1

Topic: Statistics
Series: MAY 2017

QTB – Nov 2014 – L1 – SA – Q5 – Statistics

Identifies the correct measure of relationship between variables.

Question

The measure of relationship that exists between two or more variables is known as the coefficient of:
A. Skewness
B. Variation
C. Kurtosis
D. Determination
E. Correlation

Answer

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Tags: Coefficients, Relationship, Variables
Level: Level 1

Topic: Statistics
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q4 – Statistics

Uses a regression equation to estimate the number of candidates enrolling based on total sales figures.

Question

An Accountant, with a fast food restaurant located in a professional examination centre, estimated that the regression equation relating to the total sales, y (in thousands of naira) and the number of candidates, x, that enrolled for the examination over 6 diets is given as
The number of candidates that will enrol for a particular diet if its estimated total sales is N950,000 is:
A. 160
B. 360
C. 450
D. 620
E. 700

Answer

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Level: Level 1

Topic: Statistics
Series: NOV 2014

QTB – May 2016 – L1 – SB – Q5b – Statistics

This question involves calculating the probability of a bag of Pando Yam weighing less than a specified value using the normal distribution.

Question

The weights of bags of Pando Yam produced by Swallow Company Limited are normally distributed with a mean of 3,020 grams and a standard deviation of 4 grams.

Required:
i. If a bag is picked at random, what is the probability that it weighs:

Less than 3,012 grams? (4 marks)
ii. Between 3,012 grams and 3,021.6 grams? (6 marks)
Show all the relevant normal distribution diagrams.

Answer

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Tags: Normal distribution, Pando Yam, Probability, Z-scores
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – May 2016 – L1 – SB – Q4a – Statistics

This question involves calculating expected returns from a gambler’s game of chance based on different scenarios.

Question

A gambler plays a game of chance in which he has a 60% chance of winning. If he wins, he collects N1,800, but if he loses, he pays N2,300.

Required:
i. Obtain the sample spaces respectively for 12 games and 14 games.
(2 marks)

ii. Calculate his expected returns for 12 games and 14 games.
(6 marks)

iii. Advise the gambler if he initially staked N1,000.

Answer

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Tags: Decision Making, Expected Returns, Game of Chance, Probability
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – May 2016 – L1 – SB – Q3 – Statistics

This question involves using the least squares method to fit a trend line for annual expenditures and make future forecasts.

Question

The annual expenditures (N’000) of a family from 2000 to 2009 were as follows:

Year	Expenditure (N’000)
2000	600
2001	610
2002	580
2003	590
2004	480
2005	560
2006	550
2007	620
2008	490
2009	530

Required:
a. Setting year 2000 as $x = 0$ , fit the least squares line for the annual expenditures.
(15 marks)

b. Forecast what the expenditure will be in the years:
i. 2012 (2½ marks)
ii. 2016 (2½ marks)

Answer

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Tags: Expenditure, Forecasting, Least Squares, Trend Analysis
Level: Level 1

Topic: Statistics
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

Topic: Statistics

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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 – May 2017 – L1 – SB – Q6a – Statistics

Calculate the monthly cost of replacing diodes based on failure probability and determine if a student can buy a gown based on expected money.

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QTB – May 2017 – L1 – SB – Q5b – Statistics

Calculate the Spearman's rank correlation coefficient between two accountants' rankings of ten banks.

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QTB – May 2017 – L1 – SB – Q4a – Statistics

Calculate the proportion of damaged blocks and the probability of taking a damaged block from a specific lorry using a tree diagram.

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QTB – May 2017 – L1 – SB – Q2a – Statistics

Probability calculations for dice roll and random sampling in block production.

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QTB – May 2017 – L1 – SA – Q18 – Statistics

This question calculates the centered moving average for a specific year in a time series of cocoa production.

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QTB – May 2017 – L1 – SA – Q17 – Statistics

This question checks the range of values for the correlation coefficient r.

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QTB – May 2017 – L1 – SA – Q16 – Statistics

This question asks to identify a false statement about normal distribution.

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QTB – May 2017 – L1 – SA – Q15 – Statistics

This question involves calculating the probability that a defective item is from process B.

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QTB – May 2017 – L1 – SA – Q14 – Statistics

This question involves identifying the estimable components of a time series.

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QTB – May 2017 – L1 – SA – Q13 – Statistics

This question calculates the probability of rolling either a four or a six on a six-sided die.

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QTB – Nov 2014 – L1 – SA – Q5 – Statistics

Identifies the correct measure of relationship between variables.

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QTB – Nov 2014 – L1 – SA – Q4 – Statistics

Uses a regression equation to estimate the number of candidates enrolling based on total sales figures.

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QTB – May 2016 – L1 – SB – Q5b – Statistics

This question involves calculating the probability of a bag of Pando Yam weighing less than a specified value using the normal distribution.

You're reporting an error for "QTB – May 2016 – L1 – SB – Q5b – Statistics"

QTB – May 2016 – L1 – SB – Q4a – Statistics

This question involves calculating expected returns from a gambler’s game of chance based on different scenarios.

You're reporting an error for "QTB – May 2016 – L1 – SB – Q4a – Statistics"

QTB – May 2016 – L1 – SB – Q3 – Statistics

This question involves using the least squares method to fit a trend line for annual expenditures and make future forecasts.

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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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