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# Introduction To Business Statistics Question Paper

Introduction To Business Statistics

Course:

Institution: Strathmore University question papers

Exam Year:2009

STRATHMORE UNIVERSITY

FACULTY OF COMMERCE

Bachelor of Commerce

END OF SEMESTER EXAMINATION

BCM 2105: INTRODUCTION TO BUSINESS STATISTICS

Venue: LT 2

Date: 14th October, 2009 Time: 2 Hours

INSTRUCTIONS: Answer Question ONE and any other TWO Questions

QUESTION ONE (30 marks)

a) Describe the measures of central tendency of a data set (4 marks)

b) Let x1, x2, ….,xn be n observations with corresponding frequencies f1, f2, …., fn’

Show that (i) the sum of deviations about the men is zero

(ii) Variance is not affected by change of scale (4 marks)

(c) In a statistics class of 30 students, the mean score on the mid-term test was 72. In

another class of 40 students, the mean score was 79. What is the mean for the two

classes combined? (4 marks)

e) A dairy farm company had two plots where dairy cows are kept. For one particular

day the milk yields from the two farms were as follows:

FARM 1 FARM 2

34 32 48 42 41 16 37 30 44 41

59 62 12 36 24 50 44 56 18 44

47 23 34 40 41 50 21 40 25 25

34 23 26 32 37 34 28 54 30 30

25 34 40 28 45 16 18 29 24 25 34

18 32 25 51 19 40 9 44 14 26 50

18 23 36 34 10 16 23 17 26 31 38

19 23 22 44 17 34 37

Required: Compare these data by constructing a back-to-back stem-and-leaf diagram

(6 marks)

f) Events A and B are such that P(A) = 0.3, P(B) = 0.4, P(AnB) = 0.1

Find (i) P(AnB’) Ii) P(A’nB’) (6 marks)

g) The values of random variable X and associated probabilities are given below:

x 2 3 4 5 6 7 8 9 10

p(x) 0.05 0.10 0.30 0.20 0.05 0.10 0.05 0.10 0.05

Calculate (i) E(X) (ii) E(5X + 3) (ii) Var(X) (iv) Standard deviation (6 marks)

2

QUESTION TWO (20 marks)

a) A finance analyst studied hundred companies and obtained the following data for

the year 2008:

Declared Dividends (K£’0000) Number of companies

0 – 8 10

8 – 16 20

16 – 24 16

24 – 32 19

32 – 40 15

40 – 48 10

48 – 56 6

56 – 64 4

Calculate (i) mean declared dividends (ii) Variance (iii) standard deviation of the

dividends (iv)median of number of the dividends

(12 marks)

b) At a certain University, students engage in sports in the following proportions:

Football: 40% of the total population

Hockey: 60% of total population

Both football and hockey: 30% of total population

If a student is chosen at random, calculate the probability that the student will play

(i) Football or hockey

(ii)Neither sport (6 marks)

QUESTION THREE (20 marks)

a) The data below shows yearly returns (millions) on equity of 50 companies in

2008.

165 141 163 153 130 158 119 187 185 209

177 147 166 154 159 178 187 139 180 143

160 185 153 168 189 173 127 179 163 182

171 146 174 149 126 156 155 174 154 150

210 162 138 117 198 164 125 142 182 218

Construct (i) a class frequency distribution with boundaries (ii) cumulative frequency

iii) draw a histogram (iii) draw a cumulative curve (ogive) (iv) estimate the

mode (v) estimate the median (14 marks)

b) A continuous random variable X has probability density function defined by

0 6

( )

0

kx x

f x

otherwise

?? = = =???

Find (i) value of k

(ii)P(1< x < 5)

(iii) Expected value of X

3

(iv) Variance of X (v) Standard deviation of X (8 marks)

QUESTION FOUR (20 marks)

(a) Define the terms (i) correlation coefficient (ii) coefficient of determination

(6 marks)

(b) Consider the following table that shows the amount of money used in sales and

advertisement in ten months

Employee 1 2 3 4 5 6 7 8 9 10

Length of service

(years)

6 8 9 10 11 12 14 16 18 20

Annual

income(thousands)

14 17 15 18 16 22 26 25 30 34

Required: Find (i) correlation coefficient between length of service and the annual

income.

(ii) the coefficient of determination and interpret it

(iii) the regression equation of annual income on length of service

(iii) find the annual income when the length of service is 30 years

(14 marks)

QUESTION FIVE (20 marks)

(a) The usage rate per day in units of the A category inventory item over the last sixty

days is given below.

50, 100, 100, 150, 175, 200, 150, 50, 75, 150, 125, 50, 150, 140, 130,

200, 150, 140, 60, 125, 140, 130, 150, 150, 150, 140, 160, 150, 160, 200,

50, 125, 130, 150, 150, 125, 160, 150, 140, 140, 200, 100, 75, 100, 80,

120, 140, 150, 160, 150, 160, 175, 200, 140, 150, 160, 100, 100, 150.

The stores manger has requested you to:

(i) Construct a stem-and-leaf distribution

(ii) Construct a class frequency distribution of class size 5, 40 – 45, 45 – 50,

(iii) Compute mean, variance and standard deviation

. (12 marks)

(b) The hospital administrator at Nyalo Hospital requested a management consultant

to study the amount of time a patient must wait for being treated by the

emergency staff. The management consultant collected the following data during

a typical day:

Waiting times in (minutes)

10, 4, 5, 25, 35, 15, 5, 20, 12, 15, 10, 15, 13, 11, 14, 15, 35, 2, 10, 11,

13, 32

(i) Calculate the median and the quartiles

(ii) Calculate mean and standard deviation

(iii) Draw the box plot and hence identify the outliers

(iv) Calculate the coefficient of skewness and comment (8 marks)

FACULTY OF COMMERCE

Bachelor of Commerce

END OF SEMESTER EXAMINATION

BCM 2105: INTRODUCTION TO BUSINESS STATISTICS

Venue: LT 2

Date: 14th October, 2009 Time: 2 Hours

INSTRUCTIONS: Answer Question ONE and any other TWO Questions

QUESTION ONE (30 marks)

a) Describe the measures of central tendency of a data set (4 marks)

b) Let x1, x2, ….,xn be n observations with corresponding frequencies f1, f2, …., fn’

Show that (i) the sum of deviations about the men is zero

(ii) Variance is not affected by change of scale (4 marks)

(c) In a statistics class of 30 students, the mean score on the mid-term test was 72. In

another class of 40 students, the mean score was 79. What is the mean for the two

classes combined? (4 marks)

e) A dairy farm company had two plots where dairy cows are kept. For one particular

day the milk yields from the two farms were as follows:

FARM 1 FARM 2

34 32 48 42 41 16 37 30 44 41

59 62 12 36 24 50 44 56 18 44

47 23 34 40 41 50 21 40 25 25

34 23 26 32 37 34 28 54 30 30

25 34 40 28 45 16 18 29 24 25 34

18 32 25 51 19 40 9 44 14 26 50

18 23 36 34 10 16 23 17 26 31 38

19 23 22 44 17 34 37

Required: Compare these data by constructing a back-to-back stem-and-leaf diagram

(6 marks)

f) Events A and B are such that P(A) = 0.3, P(B) = 0.4, P(AnB) = 0.1

Find (i) P(AnB’) Ii) P(A’nB’) (6 marks)

g) The values of random variable X and associated probabilities are given below:

x 2 3 4 5 6 7 8 9 10

p(x) 0.05 0.10 0.30 0.20 0.05 0.10 0.05 0.10 0.05

Calculate (i) E(X) (ii) E(5X + 3) (ii) Var(X) (iv) Standard deviation (6 marks)

2

QUESTION TWO (20 marks)

a) A finance analyst studied hundred companies and obtained the following data for

the year 2008:

Declared Dividends (K£’0000) Number of companies

0 – 8 10

8 – 16 20

16 – 24 16

24 – 32 19

32 – 40 15

40 – 48 10

48 – 56 6

56 – 64 4

Calculate (i) mean declared dividends (ii) Variance (iii) standard deviation of the

dividends (iv)median of number of the dividends

(12 marks)

b) At a certain University, students engage in sports in the following proportions:

Football: 40% of the total population

Hockey: 60% of total population

Both football and hockey: 30% of total population

If a student is chosen at random, calculate the probability that the student will play

(i) Football or hockey

(ii)Neither sport (6 marks)

QUESTION THREE (20 marks)

a) The data below shows yearly returns (millions) on equity of 50 companies in

2008.

165 141 163 153 130 158 119 187 185 209

177 147 166 154 159 178 187 139 180 143

160 185 153 168 189 173 127 179 163 182

171 146 174 149 126 156 155 174 154 150

210 162 138 117 198 164 125 142 182 218

Construct (i) a class frequency distribution with boundaries (ii) cumulative frequency

iii) draw a histogram (iii) draw a cumulative curve (ogive) (iv) estimate the

mode (v) estimate the median (14 marks)

b) A continuous random variable X has probability density function defined by

0 6

( )

0

kx x

f x

otherwise

?? = = =???

Find (i) value of k

(ii)P(1< x < 5)

(iii) Expected value of X

3

(iv) Variance of X (v) Standard deviation of X (8 marks)

QUESTION FOUR (20 marks)

(a) Define the terms (i) correlation coefficient (ii) coefficient of determination

(6 marks)

(b) Consider the following table that shows the amount of money used in sales and

advertisement in ten months

Employee 1 2 3 4 5 6 7 8 9 10

Length of service

(years)

6 8 9 10 11 12 14 16 18 20

Annual

income(thousands)

14 17 15 18 16 22 26 25 30 34

Required: Find (i) correlation coefficient between length of service and the annual

income.

(ii) the coefficient of determination and interpret it

(iii) the regression equation of annual income on length of service

(iii) find the annual income when the length of service is 30 years

(14 marks)

QUESTION FIVE (20 marks)

(a) The usage rate per day in units of the A category inventory item over the last sixty

days is given below.

50, 100, 100, 150, 175, 200, 150, 50, 75, 150, 125, 50, 150, 140, 130,

200, 150, 140, 60, 125, 140, 130, 150, 150, 150, 140, 160, 150, 160, 200,

50, 125, 130, 150, 150, 125, 160, 150, 140, 140, 200, 100, 75, 100, 80,

120, 140, 150, 160, 150, 160, 175, 200, 140, 150, 160, 100, 100, 150.

The stores manger has requested you to:

(i) Construct a stem-and-leaf distribution

(ii) Construct a class frequency distribution of class size 5, 40 – 45, 45 – 50,

(iii) Compute mean, variance and standard deviation

. (12 marks)

(b) The hospital administrator at Nyalo Hospital requested a management consultant

to study the amount of time a patient must wait for being treated by the

emergency staff. The management consultant collected the following data during

a typical day:

Waiting times in (minutes)

10, 4, 5, 25, 35, 15, 5, 20, 12, 15, 10, 15, 13, 11, 14, 15, 35, 2, 10, 11,

13, 32

(i) Calculate the median and the quartiles

(ii) Calculate mean and standard deviation

(iii) Draw the box plot and hence identify the outliers

(iv) Calculate the coefficient of skewness and comment (8 marks)

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