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: P = 12319.6 – 924A, where P is predicted price and A is age of car. Answer the following 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]

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School Business Semester 2, 2016 3 of 3

Faculty of Law, Business & Education 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 α=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]

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