From a survey of 120 students attending a university, it was found that 48 were living off campus, 57 were undergraduates, and 25 were undergraduates living off campus. One student is selected at random.
Let event A be “The student is an undergraduate”

Let event B be “The student is living off campus”.

a. Sketch the Venn diagram and show number of students for all parts of the diagram

b. Find the probability that selected person is an undergraduate student or he/she lives off campus

c. Find the probability that selected student is an undergraduate living on campus

d. Selected person is a graduate student living on campus.

The president of a University wishes to find the average age of students presently enrolled. From past studies, the standard deviation is known to be 2 years. A random sample of 50 students is selected and the mean is found to be 23.2 years.

A. Find the 95% confidence interval for the population mean.

B. Find the 99% confidence interval for the population mean?

. A teaching assistant for Statistics course as a university collected data from students in her class to investigate whether study time per week (average number of hours) differed between students who planned to go to graduate school and those who did not. The data were as follows:

Graduate school: 15, 7, 15, 10, 5, 5, 2, 3, 12, 16, 15, 37, 8, 14, 10, 18, 3, 25, 15, 5, 5

No graduate school: 6, 8, 15, 6, 5, 14, 10, 10, 12, 5.

State the null and alternative hypotheses using statistical notations. Use R command t.test to test whether study time differed between two groups. Include your R output and identify the test statistic and p-value. Draw the conclusion.

A group of high-school parents in Tucson, Arizona, in conjunction with faculty from the University of Arizona, claim that young women in the Tucson high schools not only are called on less frequently, but receive less time to interact with the instructor than do young men. They would like to see the school district hire a coordinator, spend money (and time) on faculty workshops, and offer young women classes on assertiveness and academic communication.

To make things simple, assume that instructor interactions with young men average 95 seconds, with standard deviation 35 seconds. (Treat this as population information.)

The null hypothesis will be that the average interaction time for young women will also be 95 seconds, as opposed to the alternate hypothesis that it is less, and will be tested at the 2.5% level of significance.

1. Give interpretations in context of Type I and Type II error in this situation. (Your discussion should not focus on “Null” and “Alternate”.)
2. What are the social, economic, and other consequences of (separately) Type I and Type II error?
3. Find the rejection region for this test. That is, what interaction time bounds the lower 2.5% of the distribution?
4. Assume the true mean interaction time for young women is 90 seconds. Find the power of the test.
5. Repeat part 4 for a true mean interaction time of 80 seconds.
6. What do the results in parts (4) and (5) mean in terms of your previous answers?

- Researchers from the University of Toronto Scarborough conducted two experiments that looked at the effect of two different types of motivational intervention on prejudice reduction. Summarize the two types of motivational intervention that were used in their experiments.

-If programs focusing on reducing prejudice are actually increasing prejudice, how should the issue of prejudice be addressed?

-Even though researchers now know that reducing prejudice needs to focus on motivational interventions that are more personal in nature, the authors suggest that controlling prejudice reaction practices are tempting. What benefits do controlling motivational interventions have for prejudice programs?

This comes from the Columbia University website: “As an equal opportunity and affirmative action employer, the University does not discriminate against or permit harassment of employees or applicants for employment on the basis of race, color, sex, gender (including gender identity and expression), pregnancy, religion, creed, national origin, age, alienage and citizenship, status as a perceived or actual victim of domestic violence, disability, marital status, sexual orientation, military status, partnership status, genetic predisposition or carrier status, arrest record, or any other legally protected status.”

1. Looking at this list of characteristics that Columbia doesn’t discriminate against, can you quickly put in your own words what each of them means, or are some ambiguous? If there is ambiguity, is that an ethical problem?
   
2. What’s the difference between unintentional and intentional discrimination?
   • Are some of these characteristics more vulnerable than others to unintentional discrimination? Which ones? Why?
   • Are some of these characteristics more vulnerable than others to intentional discrimination? Which ones? Why?

3. Which of the protected characteristics are concealable, meanings that in most cases a job applicant could fairly easily hide or not reveal whether he or she has the trait? Which aren’t so concealable?

Someone sent me this link to a talk by Prof. Klaus Schulten from the University of Illinois: (my emphasis)

Quantum Computing and Animal Navigation

Quantum computing is all the rage nowadays. But this type of computing may have been discovered and used by living cells billion of years ago. Nowadays migratory birds use a protein, Cryptochrome, which absorbs weak blue light to produce two quantum-entangled electrons in the protein, which by monitoring the earth's magnetic field, allows birds to navigate even in bad weather and wind conditions. The lecture tells the story of this discovery, starting with chemical test tube experiments and ending in the demonstration that the navigational compass is in the eyes and can be affected by radio antennas. The story involves theoretical physicists who got their first paper rejected as "garbage", million dollar laser experiments by physical chemists to measure the entangled electrons, and ornithologists who try to 'interrogate' the birds themselves. This work opens up the awesome possibility that room-temperature quantum mechanics may be crucial in many biological systems.

Now here's my question: What's the big deal with entangled electrons? I mean, if I do not neglect electron-electron interaction, then pretty much all electrons in a condensed matter system are entangled, are they not? Electrons in the same angular momentum multiplet are entangled via Hund's rule, electrons on neighboring sites in a tight-binding (or, in the interacting case, Hubbard) model can all be entangled due to an antiferromagnetic exchange coupling, etc. etc.

Sure, for a quantum computer I'd like to have physically separated electrons maintain their entanglement, and I'd like to have fine-grained control over which of the electrons are entangled in which way etc, but for chemical processes in molecules such as these earth-magnetic-field receptors, is it not a bit sensationalist to liken such a process to quantum computing?

This comes from the Columbia University website: “As an equal opportunity and affirmative action employer, the University does not discriminate against or permit harassment of employees or applicants for employment on the basis of race, color, sex, gender (including gender identity and expression), pregnancy, religion, creed, national origin, age, alienage and citizenship, status as a perceived or actual victim of domestic violence, disability, marital status, sexual orientation, military status, partnership status, genetic predisposition or carrier status, arrest record, or any other legally protected status.”

1. Are there any characteristics that really shouldn’t be on the list? Which ones? Why?
   
2. Hypothetically, John Smith has applied for a maintenance post at Columbia. The job entails routine and emergency plumbing and fixing of general problems, everything from burned-out light bulbs to graffiti. More or less, the job is to walk around and make sure things are in working order. He’d be working the night shift from 11 p.m. to 7 a.m. His assigned buildings would be a classroom and three coed dorms. He has been arrested three times for attempted rape of young women, but there was never enough evidence to convict.
   • Susan Rieger heads the Columbia University employment office. It’s part of her job to defend the school’s policies. In ethical terms, how do you suppose she might defend Columbia’s refusal to discriminate on the basis of arrest record?

Consider this hypothetical example. Facebook is becoming fashionable as a social medium among people, including university faculty and students. Assume the (market equilibrium) annual subscription for facebook per year is $1,200. Many faculty and students are now using it.

a) What are the private benefit to you for using facebook? (Hint: what skills will students acquire from using facebook?)

b) What are the social benefit to the faculty and student community of using facebook?

c) What are the private costs to you for using facebook?

d) What are the social costs to the faculty and student community for using facebook?

e) In your own opinion, do you think facebook would generate positive or negative externalities in the university community? Explain!

f) Should the university subsidize or tax the faculty and student use of facebook?

2. The Dean of Students at the University of Waterloo wanted to estimate the proportion of students who are willing to report cheating by fellow students. So, her staff surveyed the 172 students currently enrolled in the introduction to biology class. The students were asked, “Imagine that you witness two students cheating on a quiz. Would you tell the professor?” 19 of the surveyed students responded “yes.” (11 points total)
a. Using these data, calculate the 90% confidence interval for the proportion of all students at the University of Waterloo that would report cheating. (4 points)
b. Interpret the confidence interval from part “a” in a sentence. Interpret in terms of percentages, rather than proportions. (4 points)
c. Is it appropriate to use these data to estimate the proportion of all students at the university that would report cheating? Why or why not? (3 points)