Statistics

  Team Assessment Week #6     Name: Fatorma Bolley, Course: QRB 501     Topic 18 Exploration #3:   Age | Younger than18 years old | 18 to 24 years old | 25 to 44 Years old | 45 to 64 years old | 65 years And older | Number inThousands | 1,207,208 | 452,196 | 1,270,419 | 106,243 | 588,542 | a. Probability of age 25 to 44 is 0.2832 - 1270419/4486508   b. Probability of older than 24 is 0.6524 - (1270419 + 1068243 + 588542)/4486508   c. Median Age falls in the 45 to 64 category - 1068243        Ch. 6 #A6, #B6, 3B10 (a only):        | Musumeci Capital Management  |   |   |   |   | Probability | Return |   |   |   | MMK | 0.10 | 4% | 0.004 |   |   | Corp Bond | 0.20 | 8% | 0.016 |   |   | Eq | 0.70 | 12% | 0.084 |   |   | Expected Rate of Return | 0.104 |   |   |   |   |   |   |   |   | Expected Rate of Return | 10.4% |   |   |   |   |   |   |   |   |   |   |   |   |   |  A6.              rp = w1r1 + w2r2 + w3r3               rp = 0.10 x 4% + 0.20 x 8% + 0.70 x 12% = 10.4%   B6.              a.              Project 1:                                           Expected Return = 0.10 x 9% + 0.70 x 13% + 0.20 x 17% = 13.4%                                           σ2 = 0.10 x (9% - 13.4%)2 + 0.70 x (13% - 13.4%)2 + 0.20 x (17% - 13.4%)2 = 4.64                                           σ = 4.641/2 = 2.15%                             Project 2:                                           Expected Return = 0.10 x 3% + 0.70 x 10% + 0.20 x 22% = 8.9%                                           σ2 = 0.10 x (3% - 8.9%)2 + 0.70 x (10% - 8.9%)2 + 0.20 x (22% - 8.9%)2 = 4.49                                           σ = 4.491/2 = 2.12%                             Project 3:                                           Expected Return = 0.10 x 15% + 0.70 x 11% + 0.20 x 5% = 10.2%                                           σ2 = 0.10 x (15% - 10.2%)2 + 0.70 x (11% - 10.2%)2 + 0.20 x (5% - 10.2%)2 = 8.16                             σ = 8.161/2 = 2.86% b.    Expected Return Rank (Best to Worst): Project 1, Project 3, Project 2               Risk Rank (Best to Worst): Project 2, Project 1, Project 3 Project 1 is a good choice because it offers the lowest risk-return ratio, meaning the amount of risk taken as a percentage of return is lower than for any other project.   B10. (a)     | Returns |   |   | Probability | Stock X | Stock Y | (Probability x Return) X | (Probability x Return) Y | 0.2 | 5% | 12% | 1.00% | 2.40% | 0.2 | 10% | 10% | 2.00% | 2.00% | 0.4 | 12% | 8% | 4.80% | 3.20% | 0.15 | 14% | 0% | 2.10% | 0.00% | 0.05 | 18% | 2% | 0.90% | 0.10% | Expected Return |   |   | 10.80% | 7.70% |       Ch 7 #5:   Question: How would you conduct a reasonably reliable non probability sample'   Answer: I would conduct a reasonably reliable non probability sample of attendees for the large concert venue where I work by utilizing the quota sampling technique. I would go about conducting the quota samples by conducting a series of interviews. Some of the interviews would be face to face, while others may be via the telephone. In addition to the phone surveys, I would pulse some of the attendees of the 200 concerts via mail surveys. The reason why I choose quota sampling is because it is used to improve representativeness. The logic behind quota sampling is that certain relevant characteristics describe the dimensions of the population.   The sample size would be no more than 10% of the total number of tickets sold for the 200 live concerts featuring all types of musicians and musical groups. If the survey is conducted correctly this should yield results that are no worse than those produced by a sample based on a carefully calculated sample size. The chart below is an illustration of how, and who I would include in my sample.   Sample | Sample Size | Men | Women | Face to Face (of the Total population ) | 7.0% | 50% | 50% | Phone (of the Total population ) | 2.0% | 50% | 50% | Mail (of the Total population ) | 1.0% | 50% | 50% |   Questions to ask yourself: 1.    Can the distribution in the population be estimated' Yes        Gender: Male/Female   2.    Is this pertinent to the topic studied' Yes Concert Attendee: Music Genre    Weakness: It provides no assurance that the sample is representative of the variances being studied. The data used to provide controls may also be outdated or inaccurate. There is a practical limit on the number of simultaneous controls that can be applied to ensure precision. The choice of subjects is left to field workers to make on a judgmental basis. In other words, the people who are selected could be hand picked, and the selection criteria are somewhat objective.   Risks: Low (Systematic Bias)   Side Note: I would stay mindful of the cost to mail the surveys and the proportion of male to female individuals solicited for this survey.                         Ch 8 #31: a. What can you say about the shape of the distribution of sample mean'   The distribution of the sample mean tends to be more bell-shaped and to approximate the normal probability distribution. b.   What is the standard error of the distribution of the sample mean' The standard error =5.5/square root(25)  = 1.1         of the mean c.   What proportion of the samples will have a mean useful life of more than 36 hours'   P(X>36)=1-P(X=36)=1-P((X-35)/5.5*square root(25)34.5)=1-P(X