In this problem, we assume that the odds of giving birth to a girl or to a boy are 1 2 each. We consider a country in which, because of tradition and particular socio-economic circumstances, parents give birth to children until they give birth to their first son, at which point they stop having children. The point of the problem is to evaluate the proportion of children who are boys in a given generation. We will do this in several steps. A (3 Points) Let X be the random variable corresponding to the number of children of a given couple chosen at random in the population. What is the probability mass function of X? Verify that E[X] = 2 and Var(X) = 2 with the formulas provided at the beginning of this exam.
B (3 Points) We now assume that in the country, there are N couples who can have children, and for a given couple i, we call Xi the random variable corresponding to the number of children this couple will have. Let P be the random variable corresponding to the fraction of boys among all children. Express P in terms of X1, X2,. . . ,XN and N. Then write P in terms of the sample mean XN defined by XN = X1 +X2 +...+XN N C (2 Points) Assume the Xi are independent random variables. What is the expected value of XN and what is the variance of XN? D (4 Points) Assume N is large enough that the answer to the problem is well approximated by taking the limit N → +∞. What does the law of large numbers tell us about X
In: Statistics and Probability
The table below shows the lengths of some randomly chosen CDs in John’s very large collection. Give the 92% confidence interval for the population mean, assuming that the population is approximately normally distributed. Round the endpoints to two decimal places.
|
69.33 |
74.64 |
65.28 |
61.01 |
38.52 |
69.07 |
40.01 |
42.14 |
41.52 |
56.76 |
|
58.14 |
70.80 |
39.21 |
71.36 |
46.94 |
52.90 |
56.16 |
41.01 |
56.57 |
60.97 |
|
64.62 |
69.12 |
66.58 |
58.26 |
62.79 |
Confidence interval: ( , )
John measured the total playing time of 30 randomly chosen CDs from his very large collection and found a mean of 77.9 minutes and a standard deviation of 11.6 minutes. Give the 93% confidence interval for the population mean, assuming that the population is approximately normally distributed. Round the endpoints to two decimal places.
Confidence interval: ( , )
Studies have suggusted that twins, in their early years, tend to have lower IQs and pick up language more slowly than non-twins. The slower intellectual growth may be caused by benign parental neglect. Suppose it is desired to estimate the mean attention time given to twins per week by their parents. A sample of 34 sets of two-year-old twin boys was taken, and after one week the attention time received was recorded. The mean was found to be 32.9 hours with a standard deviation of 14.3 hours. Use this information to contruct a 98% confidence interval for the mean attention time given to all twin boys by their parents, assuming that the population is approximately normally distributed. Round the endpoints to one decimal place.
Confidence interval: ( , )
In: Statistics and Probability
Hastings Elementary School (HESH E S) is a K–5 K through 5school with 700 students. The school leader has been asked by the district superintendent to analyze the school’s most recent state-mandated assessment results to develop goals for school improvement. The school leader analyzes the assessment results for grades three through five, comparing the results with the state’s proficiency goals for all students and all student groups, to identify areas in need of improvement. State Proficiency Goals for All Students and All Student Groups Percent Proficient and Above Grade Reading Mathematics Third 65 70 Fourth 65 70 Fifth 65 70 District Vision Our vision is to ensure that all students receive an exemplary educational experience that will allow them to be competitive and productive citizens. School Goal Hastings Elementary School will meet or exceed state proficiency levels for all test grade levels. Hastings Elementary School State-Mandated Assessment Results Percent Proficient and Above All Students Special Education Students English Learners Grade Reading Mathematics Reading Mathematics Reading Mathematics Third 64 70 65 70 50 65 Fourth 70 75 60 60 55 70 Fifth 75 80 65 65 65 70 Mathematics/Reading Faculty Survey Statements Agree Disagree 1. The school’s vision and goal development process provides effective guidance for school improvement. 46% 54% 2. The school’s vision and goal monitoring process provides effective guidance and motivation for me. 55% 45% 3. I am meeting the needs of all students in my classroom. 50% 50% 4. I have sufficient resources to meet the needs of my students. 70% 30% 5. Professional development has met my educational needs. 52% 48% 6. My grade-level team meetings help improve my teaching. 75% 25% 7. My grade-level team regularly reviews mathematics and reading formative assessment results to determine trends in student misconceptions and adjust instruction. 44% 56% 8. I would benefit from additional support for improvement. 65% 35% Open-ended comments made by five or more teachers. Students receiving special education services through inclusion are sometimes struggling—not sure what to do to help them. I love using team meetings to take care of logistics, share best practices, and create common lesson plans. I struggle with the language barriers when working with my EL E Lstudents, and I’m not sure how to determine what they need next. The school leaders provide goals and choose professional development (PDP D), but sometimes I wonder why these are our goals and where the ideas for PD P Dcame from. Question Citing the data, identify and justify THREE specific goals for school improvement that the school leader should establish. For EACH goal, describe a strategy the school leader should implement and explain how the strategy will help the school leader accomplish the goal.
In: Psychology
Discussion Case: Fidelity Investments’ Partnership with Citizen Schools
Roy Fralin stood in front of a roomful of active sixth and seventh graders in an inner-city public school in Roxbury, Massachusetts. The classroom walls were covered with flip chart paper, which were packed with diagrams, numbers, and terms like “savings,” “budget,” and “investment.” A student stood at the front of the classroom. Fralin handed him a baseball cap to illustrate a loan with interest. “OK, when you give it back, you’ll owe me how much?” Another student shouted out the answer. “Great!” exclaimed Fralin. They exchanged high fives. “Now, how much are we putting away for your 401(k)?” The students punched their handheld calculators.
Fralin was not a public school teacher, and teaching personal finance to middle schoolers was not his regular job. He was a vice president and investment advisor at Fidelity Investments, where he worked mostly with high net-worth clients. But here he was, every Wednesday afternoon for 10 weeks, teaching a curriculum that Fidelity employees had developed called “How to Invest Like a Millionaire.” The program was part of a partnership between an innovative nonprofit called Citizen Schools and Fidelity Investments, one of its corporate partners. “I just don’t see any downside,” Fralin later reflected in a clip posted to YouTube about his experience as a citizen teacher. “I think this is going to be a success.”
In June 2015, Fidelity Investments was one of the leading providers of financial services in the world, administering $5.2 trillion in assets for 24 million individual and institutional clients. The company, which was privately owned, offered investment management, retirement planning, portfolio guidance, brokerage, and benefits outsourcing services. It also operated its own family of mutual funds. Fidelity maintained its headquarters in Boston, Page 415but had 10 regional operating centers and about 180 retail locations. In 2015, the firm employed 41,000 associates.
In 2009, Fidelity set about rethinking its approach to community relations. For many years, the firm had been philanthropically active, giving to a wide range of charities in its home community and elsewhere. But the company had come to believe that it could have a greater impact by focusing on partnerships with a small number of what it called “best in class” nonprofit organizations. An issue of particular concern to Fidelity was education, especially the shocking dropout rates in many of the communities it served; nationally, 1.2 million students dropped out of high school every year, many of them as early as ninth grade. In researching various options for making a difference, the company learned that the middle school years were critical in determining whether or not students would go on to graduate from high school.
To focus its resources on this issue, Fidelity chose to partner with Citizen Schools (CS). Social entrepreneur Eric Schwarz had founded CS in 1995 in Boston to operate after-school programs for middle school students, aged 11 to 14, in disadvantaged communities. The nonprofit recruited volunteer professionals—“citizen teachers”—to offer after-school apprenticeships in subjects they were passionate about in schools in the CS network. As a culminating experience, students would present what they had learned to friends, family, and teachers at what CS called “WOW!” events. In 2015, Citizen Schools had active partnerships with 29 schools in low-income communities in seven states, serving more than 4,800 students.
Fidelity had contributed money to Citizen Schools since 1998, but in 2009 it significantly stepped up its commitment and the company went beyond charity, encouraging its employees, like Roy Fralin, to teach in Citizen School programs. By 2015, Fidelity volunteers had taught more than 180 apprenticeships in such wide-ranging topics as robotics, law, and financial literacy in 34 middle schools. More than 1,500 associates had volunteered over 20,000 hours of volunteer service. Several executives served on various advisory boards. The company also donated meeting space and equipment. For example, students who had learned about web design from a Fidelity employee were invited to use the Fidelity Center for Applied Technology for their WOW! event, presenting their work in a state-of-the-art facility.
An external evaluation commissioned by Citizen Schools showed that its programs had “successfully moved a group of low-income, educationally at-risk students toward high school graduation and advancement to college, and [had] set them up for full participation in the civic and economic life of their communities.” Seventy-one percent of Citizen Schools alumni completed high school in four years, compared with 59 percent of matched peers. Sixty-one percent of students who had participated in their 8GA (8th Grade Academy) program five or more years earlier had enrolled in college, compared with 41 percent of low-income students nationally.
Fidelity indicated that in an internal survey, 89 percent of the company’s employees who had participated in the Citizen Schools partnership reported feeling more connected to their colleagues, 78 percent reported improved team-building skills, and over three-quarters reported having improved communication skills. Most importantly though, Heidi Siegal, Fidelity’s vice president for community relations, noted, “Our employees and our company enthusiastically support Citizen Schools because we know that they make a unique and significant impact on the lives of students in need.”
Sources: Corporate Voices for Working Families, “Fidelity Investments” (case study), 2012, at http://employmentpathwaysproject.org/wp-content/uploads/2014/04/Fidelity-and-Citizen-Schools-5.9.12.pdf; “Fidelity Investments,” at www.citizenschools.org/investors/current-investors/fidelity-investments; “Teaching Kids to Invest Like Millionaires,” [Roy Fralin], at www.youtube.com; “Guest Blog: At Citizen Schools, Volunteers Make STEM Relevant through Web design,” at www.educationnation.com; and private correspondence with representatives of Fidelity Investments and Citizen Schools. The website of Citizen Schools is at www.citizenschools.org. The website of Fidelity Investments is at www.fidelity.com.
Page 416
Discussion Questions
What evidence do you see in this case of the three kinds of corporate philanthropy discussed in this chapter: contributions of cash, in-kind products or services, and employee time?
What are the benefits and risks to Fidelity Investments of its partnership with Citizen Schools?
Do you consider Fidelity Investment’s partnership with Citizen Schools to be an example of strategic philanthropy, as defined in this chapter? Why or why not?
If you were a community relations manager for Fidelity Investments, how would you evaluate the impact of this partnership? What kinds of impacts would you attempt to measure, and why?
In: Economics
A sports and fitness magazine reported that the average maximum bench-press of high school varsity football players is equal to 185 pounds. A local high school football coach believes that this number is too high. He randomly samples 16 varsity high school football players from the state, which showed a mean maximum bench-press weight of 177 pounds, and a standard deviation of the sample equal to 12.5 pounds. Is the high school football coach’s claim correct? Test the hypothesis at alpha = 0.05. Assume a simple random sample and the distribution is normally distributed.
What is the P-value for this
problem?
If using “Traditional Method,” the calculated value to compare to your alpha for this hypothesis test would be equal to what?
In: Statistics and Probability
Chapter 6 in Bazerman & Moore (2013) cover how emotion and motivation influence decisions. Reconciling internal conflicts can be a challenge but keeping these elements limited when creating a strategic plan during the decision-making process is a skill that becomes transferrable to other areas of management and leadership. For your initial post, think about crisis management such as one of the recent school shootings. You are on the school board. You have small children in the school system. Discuss how you would need to keep emotions out of the planning to avoid another school shooting. What types of things need to be addressed to keep emotions away from the creation of a plan? Initial Post Length: minimum of 350 words
In: Operations Management
A researcher is interested in examining whether there are differences in students’ sense of safety across schools. She selects three schools and surveys five students from each school. The tab labeled Question 3 reflects the answers from this survey—the higher the score, the safer the student feels. Is there a difference between these schools in the students’ sense of safety?
| School A | School B | School C |
| 3 | 2 | 4 |
| 3 | 2 | 4 |
| 3 | 2 | 3 |
| 4 | 1 | 4 |
| 4 | 3 | 3 |
a. What is the null hypothesis?
b. What is the research hypothesis?
c. Why run an ANOVA statistical test?
d. What are the results of the hypothesis test? Interpret your findings. Can you reject the null hypothesis?
In: Math
Should high school athletes have to submit to random drug testing? What about students who participate in academic decathalons or cheerleading? There have been increased efforts to have all high school students complete drug testing, regardless of whether or not they play a sport. Do you think all high school students should be tested for illegal drug use? In addition do you think random drug testing will decrease illicit drug use in high school students? Why or why not? Be sure to support your position with information from your textbook, the article below, and other scholarly sources.
https://post.blackboard.com/bbcswebdav/pid-4295785-dt-content-rid-32063720_1/courses/PSY307.301086045304/Random_Drug_Testing.pdf
In: Psychology
Using the main function’s arguments, create a program that takes in a person’s name, their home town/location, and cell number then prints out the following message:
Sample run 1:
Java lab01_task03 Sililo Uis 0819876543
Output:
Contact successfully saved !!
Contact Name : Sililo @ Uis
Home number: 0819876543
In: Computer Science
Susan work at South Town Hospital. While caring for a patient, she discovered that nurse Haley has caused significant injury to a patient. Discuss the case where Haley is or is not covered under the hospital group insurance policy. (Only discuss one is covered or is not covered.). Explain with support of your reading material.
In: Nursing