## Monday, 11 May 2009

### Exercise 9.45 Business Statistics

The following is my answer to the problem 9.45 page 290 from the book "Business Statistics A First Course" by David M. Levine, Timothy C. Krehbiel and Mark L. Berenson

The Problem
You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. From past experience, you can assume that the population standard deviation is 6 minutes. A sample of 16 orders using the new delivery process yields a sample mean of 22.4 minutes.

A) At the 0.05 level of significance, is there evidence that the mean delivery time has been reduced below the previous population mean value of 25 minutes?

Z critical value from the table for α=0.05 is -1.64; -1.73 < -1.64 so the null hypothesis is rejected.
There is evidence that the mean delivery time is less than 25 minutes.

### Exercise 9.29 Business Statistics

The following is my answer to the problem 9.29 page 285 from the book "Business Statistics A First Course" by David M. Levine, Timothy C. Krehbiel and Mark L. Berenson

The Problem
The manager of a plant supply store wants to determine whether the mean amount of paint contained in 1 gallon cans purchased from a nationally known manufacturer is actually 1 gallon. You know from the manufacturer’s specifications that the standard deviation of the amount of paint is 0.02 gallon. You select a random sample of 50 cans, and the mean amount of paint per 1-gallon can is 0.995 gallon.

A) Is there evidence that the mean amount is different from 1.0 gallon (use α=0.01). Answer

Z critical value from the table for α/2=0.005 is -2.58 ; -352.558 < -2.58 so the null hypothesis is rejected.
There is evidence that the mean amount is different from 1 gallon

C) Construct a 99% confidence interval estimate of the population mean a,punt of paint. Answer

## Tuesday, 5 May 2009

### Exercise 2.3 Interactive Decision Making

The following article is my answer to the problem 2.3 page 40 from the book "Interactive Decision Making" by Liping Fang, Keith Hipel and Marc Kilgour.

The Problem
An important 2x2 game that has been extensively studied for obtaining insight into human behavior in conflict situation is called prisoner's dilemma (see, for example Rapoport, Guyer and Gordon, 1976). In this game, two people suspected of being partners in a crime are arrested and placed in separate cells so that they cannot communicate with one another. The district attorney does not have sufficient evidence to convict them for the crime. Consequently, to obtain a confession the attorney presents each suspect with the following offer:
• If one of them confess and the other does not, the one who confess can go free for cooperating with the state, while the other get a stiff 10 year sentence.
• If both prisoners confess, both get reduced sentences of five years.
• If both suspect keep silent, both go to prison for one year of lesser charge of carrying weapon.
Assuming ordinal preferences, model prisoner's dilemma using the three type of abstract game model mentioned below:

A) Normal form. Answer:

 Prisoner 2 Confess Not Confess Prisoner 1 Confess (2,2) (4,1) Not Confess (1,4) (3,3)

B) Option form. Answer:
 States 1 2 3 4 Prisoner 1 Confess Y Y N N Prisoner 2 Confess Y N Y N Normal form notation (CC) (CN) (NC) (NN)

 Preferences Vectors Prisoner 1 Y N Y N N N Y Y Prisoner 2 N N Y Y Y N Y N

C) Graph model for conflict resolution. For each decision maker, be sure to give the graph, payoff function, reachable matrix, and reachable list.

Prisoner 1

P1 = (2,4,1,3)

Prisoner 2

P2 = (2,1,4,3)

 Reachable List Initial State Prisoner 1 Prisoner 2 1 3 2 2 4 1 3 1 4 4 2 3

Please let me know in case i have made some mistakes :)