Quantitative Methods Answers

Test the significance of the values of correlation coefficient obtained from samples of size and pairs from a population. (I) r = 0·6, n = 38 (it) r = 0·5, n = 11

If the demand function of a commodity is \(Q=80-2,5P,\) where P and Q are price and quantity respectively, determine the price elasticity of demand when the price is R20. Indicate whether demand is elastic or inelastic at this price and provide justification for your answer.

1.

εd=−1,7; because |−1,7|=1,7>1, demand is elastic

2.

εd=−0,6; because |−0,6|=−0,6<1, demand is elastic

3.

εd=0,6; because |0,6|=0,6<1, demand is inelastic

4.

εd=1,7; because |1,7|=1,7>1, demand is inelastic

A bed mart company is in the business of manufacturing beds and

pillows. The company has 40 hours for assembly and 32 hours for

finishing work per day. Manufacturing of a bed requires 4 hours for

assembly and 2 hours for finishing. Similarly a pillow requires 2 hours

for assembly and 4 hours for finishing. Profitability analysis indicates

that every bed would contribute Birr 80, while a pillow contribution is

Birr 55 respectively. Find out the daily production of the company to

maximise the contribution (profit). Solve the problem by graphical

method.

A Sesotho word cannot begin with of the following letters of alphabet: D, G, V, W,

X, Y and Z.

We define the relation: A Sesotho word x is related to another Sesotho word y if x

begins with the same letter as y.

Determine whether or not this is an equivalence relation.

If it is an equivalence relation then

1. Compute C(sekatana)

2. How many equivalence classes are there in all, and why?

3. What is the partition of the English words under this relation?

If it is NOT an equivalence relation then explain in details why it is not.

Consider the statement form (P↓Q)↓R.

Now, find a restricted statement form logically equivalent to it, in

a) Disjunctive normal form (DNF).

b) Conjunctive normal form (CNF).

Consider the following premises:

1. A "\\to" (B "\\to" A) is a Theorem of Propositional Calculus/Logic (i.e. it’s logically valid),

for all statement forms A and B.

Suppose then that the following are the temporary axioms (assumptions):

a) W (axiom 1)

b) Y (axiom 2)

c) Y "\\to" Z (axiom 3)

Using the logical rules of inference, Modus Ponens (MP) and/or Hypothetical Syllogism

(HS), show that X "\\to" Z is deducible (i.e. it is a logical/valid conclusion) from the given

premises (i.e. 1 and 2).

The Star hotel was burned down in a fire and the manager decided to accommodate the guests in 4–person and 8-person tents. The tents were to be hired at a cost of Kshs 1,500 and Kshs 4,500 per night respectively, the space available could accommodate at most 13 tents and the manager had to cope with at least 64 guests.

Required Formulate this as a linear programming model that could be used to determine the number of tents of each type that could pull up in order to minimize the overall cost. (10 Marks)

Using a data of 523 workers, we obtained the following regression for model 1

Wage = -3.78 + 0.93 x Edu + 0.11 x Exper -2.41 x Female

(se) (1.2) (0.8) (0.017) (0.39)

R2 0.2492

Adj R2 0.2449

Wage: Hourly wage in $

Educ.: Education in years

Exper.: Experience in years

Female: A binary variable that takes a value of 1 for female and 0 for male

1. Interpret the coefficient of the female dummy variable in the above model. Provide your intuition in favour of your answer.

2. Using a 95% confidence interval, carry out a hypothesis test to determine whether the estimated female coefficient is significantly different from 0 at 5% level.

3. Develop a statistic to test that all the explanatory variable Educ, Exper and Female are jointly significantly different from zero. Explain your answer with suitable evidence.