part a) x = 137, s = 14.2, n = 20, H0: μ = 132, Ha: μ ≠ 132, α = 0.1

A) Test statistic: t = 1.57. Critical values: t = ±1.645. Do not reject H0. There is not sufficient evidence to conclude that the mean is different from 132.

B) Test statistic: t = 1.57. Critical values: t = ±1.729. Do not reject H0. There is not sufficient evidence to conclude that the mean is different from 132.

C) Test statistic: t = 0.35. Critical values: t = ±1.645. Do not reject H0. There is not sufficient evidence to conclude that the mean is different from 132.

D) Test statistic: t = 0.35. Critical values: t = ±1.729. Do not reject H0. There is not sufficient evidence to conclude that the mean is different from 132.

part b) A local group claims that the police issue more than 60 speeding tickets a day in their area. To prove their point, they randomly select two weeks. Their research yields the number of tickets issued for each day. The data are listed below. At α = 0.01, test the group's claim using P-values.

70 48 41 68 69 55 70 57 60 83 32 60 72 58

A) P-value = 0.4766. Since the P-value is great than α, there is not sufficient evidence to support the the group's claim.

B) P-value = 0.4766. Since the P-value is great than α, there is sufficient evidence to support the the group's claim.

part c) A local school district claims that the number of school days missed by its teachers due to illness is below the national average of μ = 5. A random sample of 28 teachers provided the data below. At α = 0.05, test the district's claim using P-values.

0 3 6 3 3 5 4 1 3 5 7 3 1 2 3 3 2 4 1 6 2 5 2 8 3 1 2 5

A) standardized test statistic ≈ -4.522; Therefore, at a degree of freedom of 27, P must lie between 0.0001 and 0.00003. P < α, reject H0. There is sufficient evidence to support the school district's claim.

B) standardized test statistic ≈ -4.522; Therefore, at a degree of freedom of 27, P must lie between 0.0001 and 0.00003. P < α, reject H0. There is no sufficient evidence to support the school district's claim

part d) To test the effectiveness of a new drug designed to relieve pain, 200 patients were randomly selected and divided into two equal groups. One group of 100 patients was given a pill containing the drug while the other group of 100 was given a placebo. What can we conclude about the effectiveness of the drug if 62 of those actually taking the drug felt a beneficial effect while 41 of the patients taking the placebo felt a beneficial effect? Use α = 0.05.

A) claim: p1 = p2; critical values z0 = ±1.96; standardized test statistic t ≈ 2.971; reject H0; The new drug is effective.

B) claim: p1 = p2; critical values z0 = ±1.96; standardized test statistic t ≈ 2.971; do not reject H0; The new drug is not effective.

We live in a connected world where communicating with people is made easier through​ technology, specifically through social networks. With the use of​ Facebook, Twitter, or​ Linked-In, you can talk to a celebrity or someone in another country as easily as you might talk to someone at your work or school. Whether your goal is business or personal​ relationships, it has never been easier to access a multitude of people quickly.
   It has been said that there are only six degrees of separation between any two people in the world. This means that any person can be connected to any other person in the world by 6 or fewer steps. For​ example, you may know someone who knows someone else who knows a person who knows someone who knows a​ celebrity, thereby linking you to the celebrity. Some have said that in our modern era of​ technology, we may even be separated by only 4 or fewer steps.
     Suppose you join an online social network and make 10 friends. Suppose that each of them has 10 friends with whom you yourself are not friends. Suppose each of those friends has 10 friends with whom you are not friends. After these 3​ steps, how many total connections do you​ have? After​ 4, 5, and 6​ steps, how many total connections do you​ have? Write a general equation that models the total number of connections after 6 steps as a function of your initial number of friends. Assume each person has the same initial number of friends. Define any variables used.
     You can reach many people in 6 steps starting with just 10​ friends, but what if you wanted to reach a number of people equal to the population of the whole​ world? How many friends would you need initially​ (and on each​ step) to connect with the number of people that is equal to the size of the entire world population in 6​ steps? Use the model and the known values to write a specific​ equation, and solve it numerically using Excel.
     Now choose a realistic number of​ people, such as the number of people at your school or in your​ town, that you want to reach in 6 steps. How many friends would you need initially​ (and on each​ step) in order to connect with this number of​ people? Use the model and the known values to write a specific​ equation, and solve it numerically using Excel. I want last part only.

Scenario #3 "What do you mean, you don't know who he is?" asked Dr. Bridewell, the head of the Oakbrook Hospital Renal Unit. ?He was unconscious when the police brought him to the ER. We started the IV, stopped his bleeding and patched him up. But he still hasn?t recovered consciousness. The police think it was a hit and run driver.? Dr. Kathy Mc Dowel spoke in a precise, matter of fact voice. Dr. Bridewell always frightened her, but she was determined not to show it. ?He didn?t have any identification?? ?No. They think somebody came along and robbed him. He was wearing jeans and a sweatshirt, nothing that gives any clue as to his background. Both of his kidneys were hopelessly damaged. But his general physical condition is good, and we think he?s a good candidate for a transplant.? ?You know we?ve got someone declared brain dead.? ?Yes, and we?ve done an HLA match.? ?We?re going to have only one kidney to transplant because the other one is shot. But I?ve got a candidate, too, so we have to decide which patient get the kidney.? ?Who?s the other candidate?? A Mrs. Benson. She?s a woman in her early sixties who?s on the school board. Her husband?s a rich lawyer, and both of them move in high social circles. She does a lot of work now with a foundation that helps minority children in school. She also happens to be a good candidate physically for a transplant.? ?So you?ll choose her over my patient?? Dr. McDowell felt herself getting angry. ?I didn?t say that. How old is this guy?? ?Early or middle thirties. He?s in good physical condition.? ?But we don?t know anything about him,? said Dr. Bridewell. ?He might just be a drifter passing through town. He?s probably not a member of the community this hospital is supposed to serve, the one that pays bills and makes donations.? ?Not that we know of,? Dr. Mc Dowell admitted. ?But we don?t know for sure, do we?? said Dr. Bridewell. Who gets the kidney? Two people need it. There is only one. Should there be a consideration of the worth of each potential recipient and their contributions to society? Would such considerations be morally correct? How would someone respond to this question using the ethical principles of:NATURAL LAW THEORIST?

Do cash incentives improve learning? A high-school teacher in a low-income urban school in Worcester, Massachusetts, used cash incentives to encourage student learning in his AP Statistics class. In 2010, 15 of the 80 students enrolled in his class scored a 5 on the AP Statistics exam. Worldwide, the proportion of students who scored a 5 in 2010 was 0.15. Is this evidence that the proportion of students who would score a 5 on the AP Statistics exam when taught by the teacher in Worcester using cash incentives is higher than the worldwide proportion of 0.15?

Conduct a hypothesis test at the significance level α = 0.05 to determine if evidence is present regarding the use of cash incentives to motivate AP Statistics students to do better on their AP exams.

Josh believes the Spanish club students at his school have an unfair advantage in being assigned to the Spanish class they request. He asked 500 students at his school the following questions: "Are you in the Spanish club?" and "Did you get the Spanish class you requested?" The results are shown in the table below:

Help Josh determine if all students at his school have an equal opportunity to get the Spanish class they requested. Show your work and explain your process for determining the fairness of the class assignment process.

5.Chromebooks.After schools closed for the remainder of the year, many school districts in Pa.were able to issue Chromebooks to families. In a random sample of 150 families in the Abington School District, 120 reported that they were able to receive Chromebooks. In a random sample of 180 families in theDowningtownAreaSchool District, 130 were able to receive Chromebooks.

a. Perform a 99% confidence intervalforthe differencein the trueproportion of families who receive Chromebooksin Abington andDowningtown School Districts.

b. Based on your interval, is there a possibility that the difference between the two true proportionscould be zero? Explain your answer.

c. Based on your previous answers, what would be your conclusion of a difference between the true proportions? (Would you fail to reject, or reject?)

1. Complete the following chart (round to two decimal places when calculating the expected values). Show all work in the space provided beneath it. (1 pt per row = 2 pts total)

WORK:

1. Suppose you are hired as a consultant to conduct a cost/benefit analysis of a proposal to power a school with 100% solar power.

a) identify all of the social benefits that you would need to estimate and classify the values (existence, extractive use, etc). Are the private benefits for the school the same as the social benefits?

b) identify all of the social costs that you would need to estimate. Are the private costs for the school the same as the social costs?

c) outline some possible ways that you could estimate the benefits and costs of the proposal

d) suppose you conduct the study and find social benefits are greater than social costs. what could be an obstacle for the school's adoption of the proposal? can you think of a solution to this problem?

Decide which of the following concepts are most applicable to each scenario: differential reinforcement of other behavior, avoidance contingency, punishment by prevention of reinforcer, punishment by loss of reinforcer, or avoidance of loss.

Defend your answer 175 words each, using citations as needed.

5. Chad continues to stay in school and is a B-minus student due to the procrastination aspect of his work ethic. He has been complaining lately about school and thinking about withdrawing. His comments about the teacher, the class, the work and his grades are starting to get annoying so his mom decides to only reinforce his verbal behavior every 5 minutes he talks to her without making a negative comment about school.