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.
b) Describe the association between age and price of a used Corolla. Do you think a linear model is appropriate?
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.
d) Why doesn't this model explain 100% of the variability in the price of a used Corolla?
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.
ii. If you want to sell a 7-year-old Corolla, what price seems appropriate?
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.
iv. You see a "For Sale" sign on a 10-year-old stating the asking price as $1500. What is the residual?
v. Would this regression model be useful in establishing a fair price for a 20-year-old car? Explain
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.
ii. within two standard deviation of the mean.
iii. below the first quartile level of demand.
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?
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.
b) What is the critical value and state the rejection rule?
c) What is the value of the test statistics?
d) What is the p-value for the test?
e) What is your conclusion?