New_or_Refurbished

New or Refurbished Kathleen Anderson QNT/561 May 28, 2012 Bonnie Merritt Cell phones have become a must have instead of a want item. When I was a teenager it was a luxury to have a cell phone, and they were rather large in size. Now that is the only telephone I have. I have even disconnected my home telephone as there is no need to have one. You do not need a telephone to have an Internet connection or a satellite connection any more, either. Now companies are selling cell phones that have been refurbished to the public so you can save even more money. That is where my dilemma comes in. Do I but a new phone that costs $500 or do I buy the refurbished phone for $150, saving me $350' My cell phone company is offering the Blackberry Curve 3G phone either brand new for $500 or I can purchase the refurbished on for $150. Research To make sure I was making a wise decision, I researched refurbished phones. I wanted to see what other people thought about them and if they have had success with them. This was easy enough to do as my cell phone company allows users to post his or her opinion right on the company’s website. They even have a ratings system of one to five stars on each of the phones, including the refurbished phones. I took a random sample from the reviews on the website from both the new phones and the refurbished phones for the Blackberry Curve 3G. Interpretation of Data To interpret my data I choose to use the Bayes’ Rule. I choose this method because I thought this was the best probability model to use to determine which type of phone to buy, a new phone or a refurbished phone. The Bayes’ Rule “relates the probability of the occurrence of an event to the occurrence or non-occurrence of an associated event,” (BusinessDictionary.com, n.d.). The Bayes’ Rule can be used to predict the probability of the satisfaction of buying a refurbished phone compared to a new phone. Once I decided on the proper theorem to use, I contacted the telephone company and discovered that 5% of users actually have returned the telephone for a different type of phone all together. With this I continued to collect my data. The variables in this experiment are: New phone = C1 = new phones rated by consumers Refurbished phones = C2 = refurbished phones rated by consumers So, what I know so far is that 5% of users return the phone; (P(C1) = returned phones = .05. Then phones kept by users is P(C2) = .95. According to the cell phone website the users’ satisfaction on level on the new phone was 90%. So, B = satisfaction of the new phone. This is written as P(B|C1) = .90. Further satisfaction of the refurbished phone is at 75% so this is written as P(B|C2) = .75. So, using Bayers’ Rule the formula looks like this: [pic] =(.05)(.9)/(.05)(.9)+(.95)(.75)=.045/.75.75=1.7125 To help us further make a decision and to ensure our information is accurate we need to plug our information into a table to check for accuracy. |Event |Prior Probability |Conditional |Joint Probability |Posterior Probability | | | |Probability | | | | |P(Ci) |P(B|Ci) |P(Ai and B) |P(Ai|B) | |Satisfied with new phone |0.05 |0.9 |0.045 |.0450 / .7575=.06 | |Satisfied with refurbished|0.95 |0.75 |0.7125 |.7125/.7575=.94 | |phone | | | | | |  |  |  |P(B) = .7575 |1 | According to the table above there is a 94% chance that I would be satisfied with a refurbished phone. Decision All decisions come with a risk. We as individuals need to determine the level of risk we are comfortable with. A 94% satisfaction is a level I would be very comfortable with. According to the cell phone website the users who bought the new cell phone are 95% satisfied, so the difference is only 1%. That is definitely a difference I can live with. The statistical tools allowed me to see that risk in a way that by just reading the reviews I would not have seen otherwise. Buying a refurbished Blackberry will save me $350, money that can be used elsewhere. As a student every penny counts and statistics and helped me save lots of pennies today! References Benson, P.G., McClave, J.T., Sincich. (2011). Statistics for Business and Economics. (11th ed.) Boston, MA: Prentice Hall. BusinessDictionary.com, (n.d.). Bayes’ Theorem. Retrieved May 24, 2012 from: http://www.businessdictionary.com/definition/Bayes-theorem.html Sprint.com (n.d.). MySprint. Retrieved May 25, 2012 from: http://www.sprint.com.