Paper 2 Quantitative Techniques.pdf

THE PUBLIC ACCOUNTANTS EXAMINATIONS BOARD A Committee of the Council of ICPAU CPA (U) EXAMINATIONS LEVEL ONE QUANTITATIVE TECHNIQUES - PAPER 2 TUESDAY 27 NOVEMBER, 2018

INSTRUCTIONS TO CANDIDATES 1.

Time allowed: 3 hours 15 minutes. The first 15 minutes of this examination have been designated for reading time. You may not start to write your answer during this time.

2.

This examination contains six questions and only five questions are to be attempted. Each question carries 20 marks.

3.

Formulae and tables are provided on pages 8 – 12.

4.

Write your answer to each question on a fresh page in your answer booklet.

5.

Please, read further instructions on the answer booklet, before attempting any question.

© 2018 Public Accountants Examinations Board

Quantitative Techniques – Paper 2

Attempt five of the six questions Question 1 (a) Explain the term ‘tables’ in terms of summarising raw data. (2 marks) (b) A dairy sold milk, in liters, on a daily basis for a period of 24 days as shown in the table below: 28 24 57 33

36 45 43 28

41 20 21 39

22 26 29 44

44 53 60 49

23 54 42 52

Required: (i)

(c)

Using a uniform class interval and starting with the class 20-24; construct a frequency distribution for the data above. (2 marks) (ii) Calculate the standard deviation for the data. (7 marks) A beverages company produced and sold crates of dry gin in the years 2016 and 2017 as shown in the following table. Month January February March April May June July August September October November December

2016 20 50 30 40 60 100 70 90 60 80 50 120

2017 30 40 50 40 50 90 110 120 80 100 70 110

Required: (i) (ii)

Construct a Z-chart for the above data. (8 marks) Comment on any feature in the Z-chart you have drawn. (1 mark) (Total 20 marks)

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Quantitative Techniques – Paper 2

Question 2 Mongoli Enterprises Ltd (NEL) deals in solar products. A routine visit by Uganda National Bureau of Standards (UNBS) established that the lifetime of the solar panels NEL sold was normally distributed with a mean of 25 years and standard deviation of 4 years. A quality controller from UNBS later visited NEL, tested a sample of solar panels and picked one at random. Required: Determine the: (i) (ii) (iii)

(b)

probability that its lifetime is greater than 18 years. (3 marks) probability that its lifetime is between 18 and 28 years. (3 marks) sample size of the panels that were tested if only two failed to exceed a life time of 18 years. (3 marks) Zakaria, a teller at Eurit Bank handles clients with bulk transactions. On a certain day, he examined a random sample of 9 transactions and noted that the mean and variance of the sample were Shs 15.2 million and Shs 5 million respectively. Required:

(c)

Determine the range of the average transaction at 95% confidence level. (4 marks) Tuge Ltd sells on average 3 motorcycles daily and the sales are believed to follow a Poisson distribution. Required: Find the probability that the motorcycle sales are: (i) exactly two. (ii) at most one. (iii) at least two.

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(2 marks) (3 marks) (2 marks) (Total 20 marks)

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Quantitative Techniques – Paper 2

Question 3 (a) (b)

Explain any one application of a regression line. (1 mark) The maize yield on a farm is believed to depend on the amount of rainfall. The values of the yield Q (tons per acre) and the rainfall P (in mm) for seven successive seasons are given in the table below. P Q

125 6.25

137 8.02

145 8.42

112 05.3

132 07.2

141 08.7

120 05.7

Required: (i)

(c)

Compute the product-moment correlation coefficient between rainfall and yield. (9 marks) (ii) Comment on the result obtained in (b) (i) above. (1 mark) A sample of six households were interviewed regarding their incomes (x) and expenditure (y). The results (in Shs ‘000’) are as shown below: x y

230 340 370 380 140 280 80 90 160 180 050 070

Required: (i) (ii)

Determine the regression equation relating y to x. (8 marks) Find the income of a household with an expenditure of Shs 60,000. (1 mark) (Total 20 marks)

Question 4 (a)

A roofing materials company produces ridges ( x ) and iron sheets ( y ) using resources according to the production function given by: x  y 2  4 y  20 . Required:

(b)

Determine the number of ridges and iron sheets produced given that for every 4 iron sheets, 1 ridge is produced. (5 marks) A famous writer of project planning textbooks would like to be paid a royalty of 15% of the sales revenue and insists the price should maximise total revenue. On the other hand the publishing company is interested in maximising profit. Given the total revenue and total cost functions are R (q )  10,000q  10q 2 and C (q)  1,000  2,500q  5q 2 respectively, where q is the number of textbooks sold.

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Quantitative Techniques – Paper 2

Required: Determine the: (i)

(c)

output that maximises total revenue and obtain the maximum royalty. (5 marks) (ii) output that maximises profit and associated royalty at that output. (6 marks) The approximate sales, in thousands of shillings, for a small retail shop in a given week are given in the probability distribution table below: Sales ( x ) Probability ( p )

100 105 110 115 120 0.01 0.08 0.20 0.50 0.21

Required: Calculate the variance for the distribution.

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(4 marks)

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Quantitative Techniques – Paper 2

Question 5 (a) (b)

Explain any two limitations of linear programming. (2 marks) Airplanes from YK airport sometimes delay to take off. The quality control manager decided to randomly choose 5 flights per day for eight days. The table below shows the number of minutes that the planes were late for takeoff. Day 1 17 03 22 06 24

Day 2 05 14 04 13 14

Day 3 12 05 06 08 04

Day 4 04 21 08 05 19

Day 5 03 09 15 35 05

Day 6 10 22 40 26 23

Day 7 02 14 13 08 12

Day 8 03 05 23 33 23

Required: (i)

(c)

Draw a control chart for the range for the above information. (8 marks) (ii) Given that the coefficients for the upper control and the lower control limits are 2.114 and 0 respectively; determine whether the process is out of control. (1 mark) An employer wants to recruit experienced workers (x) and those on probation (y) for his firm. The firm can accommodate at most 9 workers. On average, 5 hours and 3 hours of work are required of the experienced workers and those on probation respectively. The employer has to maintain an output of at least 30 hours of work per day. The rules and regulations demand that the number of experienced workers recruited should not be more than 5 times the number of those on probation. The workers union, however, emphasizes that the number of experienced workers recruited should be at least twice the number of those on probation. Required: (i) (ii) (iii)

Formulate linear inequalities from the information given. (4 marks) Illustrate the above information on a graph. (4 marks) Obtain all the possible combinations of workers that may be recruited. (1 mark) (Total 20 marks)

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Quantitative Techniques – Paper 2

Question 6 (a) (b)

Distinguish between normal costs and crash costs under network analysis. (2 marks) KA Construction Ltd is in the process of designing an improved drainage system in one of the suburbs of Kampala. The activities and duration times required are listed in precedence table below: Activity A B C D E F G

Preceding activity A A C B D E, F

Duration (days) 6 8 7 12 3 5 7

Required: (i) (ii)

(c)

(iii) (i) (ii) (iii)

Draw an activity network. (2 marks) List the possible paths through the network and their duration. (4 marks) Identify the critical path and justify your answer. (2 marks) Distinguish between the fixed base and chain base methods of computing index numbers. (2 marks) Explain three limitations of consumer price index numbers. (3 marks) The table below shows the average prices (in Shs ‘000’) for a ton of each of the following commodities in 2016 and 2017. Commodities Prices in 2016 Prices in 2017 Maize 600 700 Beans 850 900 Sorghum 520 500 Millet 550 620 Required: Calculate the simple aggregate price index for 2017 using 2016 as the base year and comment on your results. (5 marks) (Total 20 marks)

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Quantitative Techniques – Paper 2

FORMULAE 1. 2.

n! Combination nC r  (n  r )!r! n! Permutations n pr  (n  r )!

3.

Mean of the binomial distribution= np

4. 5.

Standard deviation = npq Variance of the binomial distribution  np(1  p)

6.

Standard error of population proportion S ps 

7.

Spearman’s rank correlation coefficient r  1  Product

8.

moment

coefficient

pq n 6 d 2 n(n 2  1)

of

correlation

=

n xy   x  y ( n  x 2  ( x ) 2 )  ( n  y 2  ( y ) 2 )

9. 10. 11. 12.

Cost slope

crash cost – normal cost normal time – crash time



Sample mean

x

x n

Harmonic mean (grouped data) hm 

n f

x Quartile coefficient of dispersion 

14.

Mean x  A  

16.

1

x

13.

15.

n

Harmonic mean (ungrouped data) hm 

fd

f

Q3  Q1 Q3  Q1

or

Mean x  

fx

f

N    Cfb  C Median  Lb   2  fm       d1  C Mode  lm    d1  d 2 

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Quantitative Techniques – Paper 2

17.

fx Variance Var ( x)   f

2

  fx      f  

2

 fx f

2 2

 f (x  x) f

2

18.

Standard deviation

19.

Sample standard deviation

20.

Least squares regression equation of y on x is given by; y  a  bx Where; b 

21.

  s

 (x  x)

x



2

n 1

n xy   x  y

and

n x 2   x 

2

a

 y  b x n

n

Least squares regression equation of x on y is given by; x = c +dy Where c    x

n

d y

d

and

n

22.

Standardizing normal.

23.

Confidence interval for sample mean  x  t / 2

z

n xy   x  y n  y 2  ( y ) 2

x µ 

s n

2

O  E 

24.

2  

25.

Confidence interval of proportion  p  z

E

26.

Pearson coefficient of skewness

27.

Expectation =  xP ( X  x)

28.

Laspeyres’ price index = 

29. 30.

0

pq n

( x  mode) Sk  sd

( p1  q0 )

 (q

2

 p0 )

or

  3 x  median   Sk   sd

 100

Weighted aggregate price index  

wv n

 wv

 100

0

Additive law of probability; P( A  B)  P( A)  P( B)  P ( A  B)

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Quantitative Techniques – Paper 2

FORMULAE P( A  B) Conditional probability P A B  P( B)

32.

  Independence of A, B P A B   P ( A)orP ( A  B )  P ( A)  P ( B )

33.

Continuous compounding A  P(1  r ) n 

31.

34. 35. 36.

b(1  r ) n  b r 1 1 vu  uv u Quotient rule of differentiation f  ; where f  2 v v  ( p1  q1 )  100 Paasche ' sModel   (q1  p0 ) PoissonModelP X  x   e 

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x x!

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Quantitative Techniques – Paper 2

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Quantitative Techniques – Paper 2

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