PSchool Business Semester 2, 2016 1 of 3 Faculty of Law, Business & Education QAB105 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 Semester 2, 2016 2 of 3 Faculty of Law, Business & Education 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: 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] ^ ^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] * * * * * * *