Assignment: Quantitative METHODS
Start by reading and following these instructions:
1. Quickly skim the questions or assignment below and the assignment rubric to help you focus.
2. Read the required chapter(s) of the textbook and any additional recommended resources. Some answers may require you to do additional research on the Internet or in other reference sources. Choose your sources carefully.
3. Consider the discussion and the any insights you gained from it.
4. Create your Assignment submission and be sure to cite your sources, use APA style as required, check your spelling.
Task
1. The Ashland MultiComm Services (AMS) marketing department wants to increase subscriptions for its 3-For-All telephone, cable, and Internet combined service. AMS marketing has been conducting an aggressive direct-marketing campaign that includes postal and electronic mailings and telephone solicitations. Feedback from these efforts indicates that including premium channels in this combined service is a very important factor for both current and prospective subscribers. After several brainstorming sessions, the marketing department has decided to add premium cable channels as a no-cost benefit of subscribing to the 3-For-All service.
The research director, Mona Fields, is planning to conduct a survey among prospective customers to determine how many premium channels need to be added to the 3-For-All service in order to generate a subscription to the service. Based on past campaigns and on industry- wide data, she estimates the following:
Figure 4
a. If a sample of 50 prospective customers is selected and no free premium channels are included in the 3-For-All service offer, given past results, what is the probability that
i. Fewer than 3 customers will subscribe to the 3-For-All service offer?
ii. 0 customers or 1 customers will subscribe to the 3-For-All service offer?
iii. More than 4 customers will subscribe to the 3-For-All service offer?
Suppose that in the actual survey of 50 prospective customers, 4 customers subscribe to the 3-For-All service offer.
iv. What does this tell you about the previous estimate of the proportion of customers who would subscribe to the 3- For-All service offer?
b. Instead of offering no premium free channels as in (a) above, suppose that two free premium channels are included in the 3-For-All service offer, Given past results, what is the probability that:
i. Fewer than 3 customers will subscribe to the 3-For-All service offer?
ii. 0 customers or 1 customer will subscribe to the 3-For-All service offer?
iii. More than 4 customers will subscribe to the 3-For-All service offer?
iv. Compare the results of (a) through (c) to those of 1. Suppose that in the actual survey of 50 prospective customers, 6 customers subscribe to the 3-For-All service offer.
v. What does this tell you about the previous estimate of the proportion of customers who would subscribe to the 3-For-All service offer?
vi. What do the results in (e) tell you about the effect of offering free premium channels on the likelihood of obtaining subscriptions to the 3-For-All service?
c. Suppose that additional surveys of 50 prospective customers were conducted in which the number of free premium channels was varied. The results were as follows:
Figure 5
How many free premium channels should the research director recommend for inclusion in the 3-For-All service? Explain.
2. Open EndRunGuide.pdf, the EndRun Financial Services "Guide to Investing," and read the information about the Guaranteed Investment Package (GIP). Read the claims and examine the supporting data. Then answer the following questions:
a. How accurate is the claim of the probability of success for EndRun's GIP? In what ways is the claim misleading? How would you calculate and state the probability of having an annual rate of return not less than 15%?
b. Using the table found under the "Show Me The Winning Probabilities" subhead, compute the proper probabilities for the group of investors. What mistake was made in re-porting the 7% probability claim? c. Are there any probability calculations that would be appropriate for rating an investment service? Why or why not?
3. Darwin Head, a 35-year-old sawmill worker, won $1 million and a Chevrolet Malibu Hybrid by scoring 15 goals within 24 seconds at the Vancouver Canucks National Hockey League game (B. Ziemer, "Darwin Evolves into an Instant Millionaire," Vancouver Sun, February 28, 2008, p. 1). Head said he would use the money to pay off his mortgage and provide for his children, and he had no plans to quit his job. The contest was part of the Chevrolet Malibu Million Dollar Shootout, sponsored by General Motors Canadian Division. Did GM-Canada risk the $1 million? No! GM-Canada purchased event insurance from a company specializing in promotions at sporting events such as a half-court basketball shot or a hole-in-one giveaway at the local charity golf outing. The event insurance company estimates the probability of a contestant winning the contest, and for a modest charge, insures the event. The promoters pay the insurance premium but take on no added risk as the insurance company will make the large payout in the unlikely event that a contestant wins. To see how it works, suppose that the insurance company estimates that the probability a contestant would win a Million Dollar Shootout is 0.001, and that the insurance company charges $4,000.
a. Calculate the expected value of the profit made by the insurance company.
b. Many call this kind of situation a win-win opportunity for the insurance company and the promoter. Do you agree? Explain.
4. Spurious correlation refers to the apparent relationship between variables that either have no true relationship or are related to other variables that have not been measured. One widely publicized stock market indicator in the United States that is an example of spurious correlation is the relationship between the winner of the National Football League Super Bowl and the performance of the Dow Jones Industrial Average in that year. The "indicator" states that when a team that existed before the National Football League merged with the American Football League wins the Super Bowl, the Dow Jones Industrial Average will increase in that year. (Of course, any correlation between these is spurious, as one thing has absolutely nothing to do with the other.) Since the first Super Bowl held in 1967 through 2010, the indicator has been correct 35 out of 44 times (data extracted from W. Power, "The Bulls Want Jets Grounded," The Wall Street Journal, January 22, 2011, p. B2). Assuming that this indicator is a random event with no predictive value, you would expect that the indicator would be correct 50% of the time.
a. What is the probability that the indicator would be correct 35 or more times in 44 years?
b. What does this tell you about the usefulness of this indicator?
5. According to a Virginia Tech survey, college students make an average of 11 cell phone calls per day. Moreover, 80% of the students surveyed indicated that their parents pay their cell phone expenses (J. Elliot, "Professor Researches Cell Phone Usage Among Students", February 26, 2007).
a. What distribution can you use to model the number of calls a student makes in a day?
b. If you select a student at random, what is the probability that he or she makes more than 10 calls in a day? More than 15? More than 20?
c. If you select a random sample of 10 students, what distribution can you use to model the proportion of students who have parents who pay their cell phone expenses?
d. Using the distribution selected in (c), what is the probability that all 10 have parents who pay their cell phone expenses? At least 9? At least 8?
Format your assignment according to the following formatting requirements:
1. The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
2. The response also includes a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.
3. Also include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.
Attachment:- Quantitative-METHODS.rar