QAB 105 -Assignment-Quantitative Analysis for Business

Assignment : QAB 105 Quantitative Analysis for Business
Due date:

Week 11, Friday, 7 October 2016, 5pm CST

Value:

25%

Lecturer/
Tutor:

Dr Bala K Nadarajah

Task

Answer all assignment questions.

Presentation

Eligible handwriting or typed.

School Business
Faculty of Law, Business & Education

Semester 2, 2016
1 of 3
QAB105 Quantitative Analysis for Business

Question 1
Classified ads in the Australian offered several used Toyota Corollas for sale. Listed below are
the ages of the cars and the advertised prices.
Age (yr)

Prices Advertised ($)

1

12995, 10950

2

10495

3

10995, 10995

4

6995, 7990

5

8700, 6995

6

5990, 4995

9

3200, 2250, 3995

11

2900, 2995

13

1750

a) Make a scatterplot for these data.
[1 Marks]
b) Describe the association between age and price of a used Corolla. Do you think a linear
model is appropriate?
[2 Marks]
c) Computer software says that r 2 = 0.894. What is the correlation between age and price?
Explain the meaning of r 2 in this context.
[2 Marks]
d) Why doesn’t this model explain 100% of the variability in the price of a used Corolla?
[1 Marks]
e) Given the estimated linear model for the relationship between a car’s age and its price is:
^ = 12319.6 – 924A, where ^P is predicted price and A is age of car. Answer the following
P
questions:
i.

Explain the meaning of the slope of the line, and the y-intercept of the line.
[2 Marks]

ii.

If you want to sell a 7-year-old Corolla, what price seems appropriate?
[1 Marks]

iii.

You have a chance to buy one of two cars. They are about the same age and appear
to be in equally good condition. Would you rather buy the one with a positive residual
or a negative residual? Explain.
[2 Marks]

iv.

You see a “For Sale” sign on a 10-year-old stating the asking price as $1500. What is
the residual?
[2 Marks]

v.

Would this regression model be useful in establishing a fair price for a 20-year-old
car? Explain
[2 Marks]

School Business
Faculty of Law, Business & Education

Semester 2, 2016
2 of 3
QAB105 Quantitative Analysis for Business

Question 2
If Tennant Creek Town’s daily water demand is approximately normally distributed with
a mean of 5 ml and a standard deviation of 1.25ml:
a) Estimate the number of days in a (365 day) year on which daily consumption is:
i. 50% or more greater than the mean.
[1 Marks]
ii. within two standard deviation of the mean.
[1 Marks]
iii. below the first quartile level of demand.
[1 Marks]
b) If the water supply authority decides to save money by setting supply capacity to a
level adequate to satisfy daily demand on 95% of all days at what level should
capacity be set?
[2 Marks]

Question 3
An executive of a new telephone company wants to know whether the average length
of evening long-distance telephone calls in a metropolitan area still equals 18.1
minutes, as it did in the past. A simple random sample of 25 evening calls is to be
used to find the answer at a significance level of ?=0.05. After taking a sample of
n = 25, the statistician finds a sample mean duration of calls of 17.2 minutes and
sample variance of 4 minutes squared.
a) Formulate the null and alternative hypothesis.
[1 Marks]
b) What is the critical value and state the rejection rule?
[1 Marks]
c) What is the value of the test statistics?
[1 Marks]
d) What is the p-value for the test?
[1 Marks]
e) What is your conclusion?
[1 Marks]

*******

School Business
Faculty of Law, Business & Education

Semester 2, 2016
3 of 3
QAB105 Quantitative Analysis for Business