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 2015 – L1 – SB – Q5a – Statistics

This question involves calculating the probabilities of various scenarios of success for two independent businesses using probability theory.

Question

a. The probability that business A succeeds is 0.65 while the probability that business B
succeeds is 0.75. If the successes of the two events are independent, obtain the
probability that
i. either business A or business B or both businesses succeed (4 Marks)
ii. only one of the businesses succeeds (3 Marks)
iii. none of the two businesses succeed (3 Marks)

Answer

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Tags: Business Success, Independent Events, Probability
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – Nov 2015 – L1 – SA – Q14 – Statistics

This question asks for the type of correlation exhibited in a scatter plot where the price and quantity have a downward trend.

Question

The scatter plot depicting the association that exists between the price of an item and the quantity supplied is such that all the points fall on a straight line and their movement is in a downward trend. This type of correlation exhibited in the graph is known as:

A. Perfect positive
B. Positive
C. Perfect negative
D. Negative
E. Zero

Answer

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Tags: Correlation, Negative Correlation, Scatter Plot
Level: Level 1

Topic: Statistics
Series: NOV 2015

QTB – Nov 2015 – L1 – SA – Q13 – Statistics

This question asks for the calculation of the 3-day moving average for a given data set.

Question

he table below shows the quantity of newspapers sold daily in a week by a vendor:

Days of the Week	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
Quantity Sold	550	450	500	370	420	620	490

The 3-day moving average corresponding to Friday is:

A. 400
B. 430
C. 470
D. 550
E. 570

Answer

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Tags: Forecasting, Moving Average, Sales
Level: Level 1

Topic: Statistics
Series: NOV 2015

QTB – Nov 2015 – L1 – SA – Q12 – Statistics

This question asks for the measure that explains how well the regression line fits the data.

Question

The measure that explains how well the regression line fits a set of data on daily sales of a product is known as coefficient of:

A. Rank Correlation
B. Product-Moment Correlation
C. Determination
D. Variation
E. Linear Regression

Answer

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Tags: Coefficient of Determination, Correlation, Regression Line
Level: Level 1

Topic: Statistics
Series: NOV 2015

QTB – Nov 2015 – L1 – SA – Q11 – Statistics

This question calculates the area under the normal curve based on the given Z-score.

Question

If the z-score for a normal distribution is 1.89, then the area under the normal curve to the right of z is:

A. 0.02
B. 0.03
C. 0.04
D. 0.47
E. 0.97

Answer

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Tags: Normal distribution, Probability, Z-Score
Level: Level 1

Topic: Statistics
Series: NOV 2015

QTB – Nov 2015 – L1 – SA – Q10 – Statistics

This question explains the concept of random experiments in probability analysis.

Question

Random experiments in probability analysis are experiments whose outcomes:

A. Cannot be predicted
B. Cannot be predetermined
C. Cannot be easily determined
D. Cannot be biased
E. Can be determined from records

Answer

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Tags: Probability Analysis, Random Experiments
Level: Level 1

Topic: Statistics
Series: NOV 2015

QTB – Nov 2015 – L1 – SA – Q9 – Statistics

This question explores the importance of probability in business decision-making.

Question

Probability is important in business because most decision-making in business involves:

A. Mutually exclusive situations
B. Most-likely situations
C. Equally-likely situations
D. Uncertainty situations
E. Certainty situations

Answer

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Tags: Business Decision-Making, Probability, Uncertainty
Level: Level 1

Topic: Statistics
Series: NOV 2015

QTB – May 2015 – L1 – SA – Q20 – Statistics

Calculating the inter-quartile range for the weekly wages of employees.

Question

If the weekly wages of 5 employees at XYZ company are N10,000, N8,500, N7,500, N6,000, and N5,200, the inter-quartile range for the weekly wages is:

A. N3,450
B. N3,650
C. N3,850
D. N4,050
E. N4,250

Answer

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Tags: Inter-Quartile Range, Statistical Analysis, Weekly Wages
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q19 – Statistics

Identifying the components separated during the deseasonalisation of business data.

Question

Deseasonalisation of business data is a process of separating two components of a time series which are:

A. Trend and cyclical variation
B. Irregular and cyclical variation
C. Trend and seasonal variation
D. Cyclical and seasonal variation
E. Seasonal and irregular variations

Answer

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Tags: Deseasonalisation, Statistical Analysis, Time series
Level: Level 1

Topic: Statistics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q18 – Statistics

Identifying the term for the locus of mid-points of a histogram.

Question

The locus of the mid-points of the tops of the rectangles in the constructed histogram by a straight line is known as:

A. Ogive
B. Frequency polygon
C. Component bar chart
D. Pictogram
E. Histogram

Answer

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Tags: Data Visualization, Frequency Polygon, Histogram
Level: Level 1

Topic: Statistics
Series: MAY 2015

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.

You're reporting an error for "QTB – May 2017 – L1 – SA – Q17 – Statistics"

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 2015 – L1 – SB – Q5a – Statistics

This question involves calculating the probabilities of various scenarios of success for two independent businesses using probability theory.

You're reporting an error for "QTB – May 2015 – L1 – SB – Q5a – Statistics"

QTB – Nov 2015 – L1 – SA – Q14 – Statistics

This question asks for the type of correlation exhibited in a scatter plot where the price and quantity have a downward trend.

You're reporting an error for "QTB – Nov 2015 – L1 – SA – Q14 – Statistics"

QTB – Nov 2015 – L1 – SA – Q13 – Statistics

This question asks for the calculation of the 3-day moving average for a given data set.

You're reporting an error for "QTB – Nov 2015 – L1 – SA – Q13 – Statistics"

QTB – Nov 2015 – L1 – SA – Q12 – Statistics

This question asks for the measure that explains how well the regression line fits the data.

You're reporting an error for "QTB – Nov 2015 – L1 – SA – Q12 – Statistics"

QTB – Nov 2015 – L1 – SA – Q11 – Statistics

This question calculates the area under the normal curve based on the given Z-score.

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QTB – Nov 2015 – L1 – SA – Q10 – Statistics

This question explains the concept of random experiments in probability analysis.

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QTB – Nov 2015 – L1 – SA – Q9 – Statistics

This question explores the importance of probability in business decision-making.

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QTB – May 2015 – L1 – SA – Q20 – Statistics

Calculating the inter-quartile range for the weekly wages of employees.

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QTB – May 2015 – L1 – SA – Q19 – Statistics

Identifying the components separated during the deseasonalisation of business data.

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QTB – May 2015 – L1 – SA – Q18 – Statistics

Identifying the term for the locus of mid-points of a histogram.

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