Twelve-year-old Aiden loved soccer. That’s why it was sheer torture for him to miss even a minute of recess. All morning long, he waited for the chance to escape his classroom and run to the field outside his school to play during lunchtime. Unfortunately, today Aiden was late for recess because he had “lunch duty” and it was his responsibility to make sure the tables were clean after everyone had eaten. When he was finished, Aiden dashed to the soccer field. Dismayed, he discovered that the other boys had already started and were in the middle of a close game. “Which team should I be on?” Aiden asked one of the boys. The boy responded curtly, “Neither. Take a seat.” Another boy said, “Yeah. The game’s too close.” Several other boys snickered and then ran off after the ball. Aiden felt a rush of warmth spread from the middle of his chest to the center of his face. He didn’t know exactly how he felt. Was it pain? Disappointment? Rejection? Anger? Whatever the feeling, it was not good and Aiden knew he needed to do something about it.

1. Identify the six main components of Crick and Dodge’s (1994, 1996) socialinformation processing model.

2. If Aiden was a boy with a history of reactive aggression, what sort of biases might he show in his social information processing?

3. If Aiden was a boy with a history of proactive aggression, what sort of biases might he show in his social information processing?

4. After Aiden enacts his solution to this social problem, how does the social information-processing model repeat itself?

5. If you were Aiden’s therapist, how might you use problem-solving skills training (PSST) to help him avoid conflicts with peers?

The National Assessment of Educational Progress (NAEP) gave a test of basic arithmetic and the ability to apply it in everyday life to a sample of 840 men 21 to 25 years of age. Scores range from 0 to 500; for example, someone with a score of 325 can determine the price of a meal from a menu. The mean score for these 840 young men was x¯¯¯x¯ = 272. We want to estimate the mean score μμ in the population of all young men. Consider the NAEP sample as an SRS from a Normal population with standard deviation σσ = 60.

(a) If we take many samples, the sample mean x¯¯¯x¯ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score μμ in the population. What is the standard deviation of this sampling distribution?
(b) According to the 95 part of the 68-95-99.7 rule, 95% of all values of x¯¯¯x¯ fall within _______ on either side of the unknown mean μμ. What is the missing number?
(c) What is the 95% confidence interval for the population mean score μμ based on this one sample? Note: Use the 68-95-99.7 rule to find the interval.

2.

The National Institute of Standards and Technology (NIST) supplies "standard materials" whose physical properties are supposed to be known. For example, you can buy from NIST a liquid whose electrical conductivity is supposed to be 5. (The units for conductivity are microsiemens per centimeter. Distilled water has conductivity 0.5.) Of course, no measurement is exactly correct. NIST knows the variability of its measurements very well, so it is quite realistic to assume that the population of all measurements of the same liquid has the Normal distribution with mean μμ equal to the true conductivity and standard deviation σσ = 0.2. Here are 6 measurements on the same standard liquid, which is supposed to have conductivity 5:

5.32   4.88   5.10   4.73   5.15   4.75

NIST wants to give the buyer of this liquid a 96% confidence interval for its true conductivity. What is this interval?

3.

Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district:

These 31 girls are an SRS of all seventh-grade girls in the school district. Suppose that the standard deviation of IQ scores in this population is known to be σσ = 15. We expect the distribution of IQ scores to be close to Normal. Estimate the mean IQ score for all seventh-grade girls in the school district, using a 98% confidence interval.

3.

How heavy a load (pounds) is needed to pull apart pieces of Douglas fir 4 inches long and 1.5 inches square? Here are data from students doing a laboratory exercise:

Suppose that the strength of pieces of wood like these follows a Normal distribution with standard deviation 3000 pounds. Give a 99% confidence interval for the mean load required to pull the wood apart.

to  lb

Suppose a research team is interested in the behavioral ramifications that may develop from women and young girls receiving the HPV vaccine at an early age. The research hypothesis is that women and girls that receive the vaccine are less likely to follow federal recommendations that mandate these women to undergo regular screening for cervical cancer. The research team decides to investigate this relationship by following a group of women and girls aged 12-21 for up to 10 years and observing their behaviors in relation to cervical screening. The team receives a list of women and girls in this age range from their local legislators, and divides the group into 4 different age ranges. The team then sampled 100 women and girls from each age range and followed them for the full study period. What type of study design is this? Is there a sampling methodology use and if so what kind? What are the exploratory and response variables?

For each problem below, state the distribution, list the parameter values and then solve the problem. You may use Excel to solve but you still need to list the distribution name and parameter value(s). For example: Poisson distribution, x=5, ?=0.24, P(5; 0.24) = 0.78

a) A skeet shooter hits a target with probability 0.5. What is the probability that they will hit at least four of the next five targets?

b) You draw a random sample of 15 first graders to participate in a survey, from a class of 39 which has 19 boys and 20 girls. What is the probability that seven of the students selected will be boys?

c) You are given an unlimited number of chances to complete a very difficult problem, but your grade will be lowered each chance you take. Past history says that you have a 30% chance of getting it right. What is the probability that you will get it right on the third try?

Use the following to solve parts d through g

Cars in Miami are sold at a rate of 1.13 per day and on average 12.3% of the cars sold are considered “old” – that is they are model year 2007 or older. It seems to you – a car dealer – that the number of cars and the number of buyers and sellers in the market are very large this month compared to other moths. You decide that age of cars, number of sales and time until next sale are independent across time periods.

d) Find the probability that exactly 1 of the next 7 cars sold will be an “old” car.

e) Find the probability that exactly 9 cars will be sold in the next 7 days.

f) What is the probability that it will be at least 8 days before the next car is sold?

g) Suppose no cars are sold in March. What is the probability that no cars will be sold in the first 7 days of April?

The assignment is directly below-- Its a public policy question, with some calculations based on discounting-- Read below

As you know, Soundville currently has no municipal trash collection and so residents must either burn their trash individually or take it to one of several transfer stations located around the town. Recent legislation has put restrictions on the outside burning of trash in populated areas, and residents of the town have been complaining about the inconvenience of carrying their own trash to the transfer stations. And the town is growing; recent mid-decade census estimates show that we are now the largest town in North Carolina that has no municipal trash collection system.

The town council has assigned me the task of asking you to analyze three different proposals for trash collection. I will need your report by February 10.

The first proposal entails the town organizing a sanitation department. Projections show that the town would need one garbage truck, costing $100,000 with annual maintenance costs of $18,000. Two new town employees whose salaries and benefits would cost $22,000 per year per employee would need to be hired. A supervisor would be necessary at salary and benefits project­ed to run about $45,000 per year. The truck would reach the end of its useful life in fifteen years and thus would need to be replaced with a new truck costing about the same amount of money (pre-discounted). This proposal would include once a week back door (meaning that trash cans would not have to be put on the curb) trash collection.

The second proposal would involve buying a automated side load (ASL) garbage truck. The manufacturer of this truck says that it is so advanced that a sanitation supervisor would be unnecessary and I could take on the few additional duties of supervising sanitation. However, since I would be performing these duties in addition to my normal duties, a new part-time administrative assistant would need to be hired at a salary of $11,000 per year (no benefits for part-time employees). There would only need to be one new sanitation employee hired at the same rate as above. Rather than $100,000, the new truck would cost $185,000 and would have slightly higher annual maintenance costs of $20,000. This truck’s useful life is promised to be ten years so it would need to be replaced after each ten-year cycle. This proposal would include once a week curbside trash collection. Residents would be supplied with special garbage containers at no cost; the city paying a one-time fee of $12,000 for the cans.

The third proposal entails contracting with a private company for trash collection. Waste Disposal Inc. (WDI) has indicated to the town that it would provide trash collection services on a contract basis for a fee of $175,000 per year. Their bid assumes twice a week curbside trash collec­tion. Residents would be supplied with special garbage containers as part of the WDI contract (at no cost to residents).

You should assume a 30 year time frame for your compari­sons and a 3% discount rate.

Looking only at the total cost to the town government, which of these three alternatives would you recommend to the council? If you added a second criterion of effectiveness of garbage removal (defined as how often garbage is picked up), what would your recommendation be? If you added a third criterion of residents’ convenience (defined as how little work residents must do to dispose of garbage) what would your recommendation be?

The council is also interested in whether this is an exhaustive list of options for trash disposal in Soundville. If you can develop any other ideas please list them and, if the council finds them interesting, they may ask you to analyze those against the three given options

A new aerated sewage lagoon is required in a small town in 2020. In 2015, one was built on a similar site in a nearby city for $3 million.The new lagoon is 75% larger, and its power sizing exponent is 0.90. The cost index for 2015 is 180, whereas the one in 2020 is 400. Estimate the cost of new lagoon in 2020.

1.   Describe what type of data analysis would use linear correlation coefficients and line of best fits. Describe the benefits of comparing to a line of best fit. (10 points)

2. Raw data is found in the excel file titled “STA322 Week 3 Data – Tab Line of Best Fit.” Calculate the linear correlation coefficient of that data and describe what that information provides. Find the slope and y intercept and list the line of best fit. Take Microsoft Excel and graph this line of best fit, using the “trend” function. Determine how you will implement the results you received to improve the data, base it on a scenario for your career. (30 points)

3. Express the likelihood given as a probability between 0 and 1 for the following (20 points):

                a. The Weather Channel stated that we have a 75% chance of being hit by the hurricane.

                b. I have a 22% chance of winning the Sweepstakes.

                c. When playing Yahtzee, I can roll 1 die and I need a 4. What are my chances?

                d. The gender of the new baby being a girl.

4. A survey was taken at a K-6^th grade school. Do you have enough time at lunch? Given the table below, answer the following questions (20 points):

If b represents the event of selecting a response from a boy, find P(Ђ).

Find the probability that the selected answer was made by a girl or was answered no.

If g represents the event of selecting a response from a girl, find P (ḡ).

Find the probability that the selected answer was made by a boy and answered yes.

5. Find the number of ways that 6 Discussion responses can be ordered by calculating 6! (5 points)

6. Find the number of ways that the 5 children can line up to go to recess by calculating 5! (5points)

Use Permutations or Combinations on the next 3 examples:

7. If you are allowed to use numbers 1 – 20 and need to choose the passcode of an exact 4 digit code, how many possibilities are there? (10 points)

8. If there are 25 students in the class and we need to select a President and Secretary for our meetings, how many possibilities are there? (10 points)

9. In playing a card game, I am dealt 6 cards, how many possibilities are there for my hand? (10 points)

A clinical trial was conducted using a new method designed to increase the probability of conceiving a boy. As of this​ writing, 297 babies were born to parents using the new​ method, and 241 of them were boys. Use a 0.01 significance level to test the claim that the new method is effective in increasing the likelihood that a baby will be a boy. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method and the normal distribution as an approximation to the binomial distribution.

The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts​ (a) through​ (d) below.

Click the icon to view the table.

a. Find the probability of getting exactly 6 girls in 8 births.

nothing

_____ ​(Type an integer or a decimal. Do not​ round.)

number of girls (x) P(x)

The population of a town A is less than the population of town B. However, the population of town A is growing faster than the population of town B. Write a program that prompts the user to enter the population and growth rate of each town. The program outputs after how many years the population of town A will be greater than or equal to the population of town B and the populations of both the towns at that time. (A sample input is: Population of town A = 5000, growth rate of town A = 4%, population of town B = 8000, and growth rate of town B =2%.)

Hint: The population can be calculated as the following:

,??-????????????.=,??-??????????????.?(1+??????????? ????????/100.0)