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Hps2205:Quantitative Methods Question Paper
Hps2205:Quantitative Methods
Course:Bachelor Of Commerce
Institution: Meru University Of Science And Technology question papers
Exam Year:2012
QUESTION ONE (30 MARKS)
a) Explain the meaning of the following terms: i. Leontiff matrix (2 Marks) ii. Markorian process (2 Marks) iii. Singular matrix (1 Mark) iv. Type one and type two errors (2 Marks) b) Find the inverse A-1 of matrix A, given that
A=
1 1 1 3 1 3 1 2 3 (4 Marks)
c) Differentiate with respect to both x and y: Z = 5222+ 3 (4 Marks)
d) Determine (32 3 1
+ 3) (3 Marks)
e) The height of maize plants grown in Katheri location in the Meru County is normally distributed with mean (µ) of 180 cm and a standard deviation of 15 cm. If a maize plant is selected at random from a farm there, what is the probability that its height will be: i. Less than 160 cm (2 Marks) ii. Between 170 cm and 195 cm (3 Marks) iii. If in Katheri location, 500,000 plants are grown, how many plants are expected to have a height of 193 cm and 207 cm. (3 Marks)
f) The probability that a share price rises from one day to the next is 0.45. A portfolio contains 80 different shares. Calculate the probability that the share prices of 30 companies rise in that day? (4 Marks)
QUESTION TWO (20 MARKS)
a) i. Distinguish between correlation and regression. (2 Marks) ii. Competitors in a contest were ranked by two judges in the following order.
Judge 1
24 28 27 26 25 29 30 23 22 23
Judge 2
26 27 28 24 25 30 29 22 23 24
Use rank correlation to comment on the results of the two judges. (5 Marks)
b) A random sample of 130 undergraduate and 90 graduate students was taken. Among the undergraduates 36% say that the computing facilities t adequate whereas 29% of the post graduate adequate. i. Construct 95% confidence interval of the difference between the opinions of the two groups of students. ii. By testing hypothesis, determine whether there is a significant difference between the opinions of the two groups. (7 Marks) c) Intelligence tests given to two groups of boys and girls gave the following information.
Number Mean Score Standard Deviation Girls Boys 50 100 75 70 10 12
Is the difference in the mean scores of boys and girls statistically significant? (4 marks)
d) Highlight the properties of good estimators (2 Marks)
QUESTION THREE (20 MARKS)
a) The advertising expenditure and sales for 10 business firms is as shown below
Firm 1 2 3 4 5 6 7 8 9 10 Advertising Expenditure(Ksh. 000) x 57 54 49 42 38 32 30 24 20 18 Sales Revenue) y 113 111 107 103 100 96 94 84 74 76
i. Calculate the coefficient of correlation and comment on the results ( 5 Marks)
ii. Find the regression equation of sales revenue on advertising expenditure using the simple linear regression. (5 Marks)
iii. Estimate the sales revenue of the business firm if advertising expenditure is Ksh. 26.000 (1 Mark)
b) Solve
x + 2y +3z = 3
2x + 4y + 5z = 4
3x + 5y + 6z= 8 (5 Marks)
c) A transition matrix of retentions gains and losses of firms A, B and C is given as
0.7 0.1 0.2 0.1 0.8 0.1 0.2 0.1 0.7 Determine the steady state equilibrium conditions (4 Marks)
QUESTION FOUR (20 MARKS)
a) A training director is interested in knowing if there is a significant difference in the effectiveness of three methods tried on 16 new employees using records of their daily production.
Method 1 15 18 19 22 11 Method 2 22 27 18 21 17 Method 3 18 24 19 16 22 15
Test this hypothesis based on the information. (Hint: use Anova test) (10 Marks)
b) An economy consists of two industrias R and S. Analysis of their operation indicate that Ksh. 1 worth of output from R requires input worth 15 cents from itself and 10 cents from S. On the other hand Ksh 1 worth of output from S requires input worth 20 cents from R and 25 cents from S. It is projected that external demand from R will be worth Ksh 200 m and from S will be Ksh 500 m.By coming up with an input output model, determine the total output worth from the two businesses to satisfy the requirement. (10 Marks)
QUESTION FIVE (20 MARKS)
a) A production firm claims that it has improved the quality of new animal feeds. Out of 29 cattle of the same breed that were given the new feed, 16 cattle produced 36l of milk on average per day with a standard deviation of 3.6L. The remaining 13 cattle produced an average of 33.5 L of milk per day with s.d = 4.2L. Can the
Hint: Use T test (6 Marks)
b) Find the partial derivatives of i. = 2 2+ (4 Marks) ii. = (32 + 3)5 (4 Marks)
c) The demand are total cost function for a firm are given by P = 140 2Q TC = 10 + 52
Find the firms expressions for:
i. TR ii. MR iii. Find the firms profit maximizing quantity and price (6 Marks)
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