1. Which of the following statements best describes a sampling distribution?

Select one:

a. It is the distribution of the values of a variable in the population from which the sample is taken

b. It is the distribution of the values of a statistic that resembles the normal distribution when the sample size is large

c. It is the distribution of the values of a statistic calculated from 1000 simple random samples displayed in a histogram.

d. It is the distribution of the values of a particular variable that are observed in a random sample.

2. The weight of extra-large egg has a Normal distribution with a mean of 3 oz and a standard deviation of 0.1 oz.

What is the sampling distribution of the mean weight of extra-large egg (i.e., the distribution of the sample mean weight of an egg in a randomly selected carton of a dozen eggs (i.e., 12 eggs))?     

Select one:

a. N(12,1)

b. N(3, 0.1)

c. N(3, 0.03)

d. N(3, 0.2)

3. The manager at a movie theater would like to estimate the true mean amount of money spent by customers on popcorn only. He selects a simple random sample of 26 receipts and calculates a 92% confidence interval for true mean to be ($12.45, $23.32). The confidence interval can be interpreted to mean that, in the long run,                   

Select one:

a. 92% of all customers who buy popcorn spend between $12.45 and $23.22

b. 92% of similarly constructed intervals would contain the population mean

c. 92% of similarly constructed intervals would contain the sample mean

4. A population variable has a distribution with mean µ = 25 and variance σ² is 256. From this population a simple random sample of n observations is to be selected and the mean of the sample values calculated. If the population variable is known to be Normally distributed and the sample size is to be n = 25, what is the probability that the sample mean will be between 20.5 and 31.50, i.e., P(20.5 ≤ x-bar ≤ 31.5)?

5. Since confidence intervals are based on the sampling distribution of the sample mean, it is possible to form confidence intervals when sampling from slightly skewed distributions due to the central limit theorem

Select one:

True

False

6. The heights of a simple random sample of 200 male high school sophomores in a midwestern state are measured. The sample mean (x-bar) is 70 inches. Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation is 5 inches.    

What is a 99% confidence interval for the population mean μ?

Select one:

a. (59.46, 72.94)

b. (69.09, 70.91)

c. (65.67, 66.73)

d. (58.16, 74.24)

7. The heights of a simple random sample of 200 male high school sophomores in a midwestern state are measured. The sample mean (x-bar) is 70 inches. Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation of σ is 5 inches.

Suppose the heights of a simple random sample of 100 male sophomores were measured instead of 200. Which of the following statements is true?  

Select one:

a. The margin of error for the 95% confidence interval would decrease

b. The margin of error for the 95% confidence interval would increase

c. The standard deviation would decrease

A study was done to look at the relationship between number of movies people watch at the theater each year and the number of books that they read each year. The results of the survey are shown below.

1. Find the correlation coefficient: r=r=    Round to 2 decimal places.
2. The null and alternative hypotheses for correlation are:
   H0:H0: ? μ ρ r  == 0
   H1:H1: ? ρ μ r   ≠≠ 0
   The p-value is:      Round to 4 decimal places.
   
   
   
   
   
3. Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study.
   • There is statistically significant evidence to conclude that a person who watches more movies will read fewer books than a person who watches fewer movies.
   • There is statistically significant evidence to conclude that a person who watches fewer movies will read fewer books than a person who watches fewer movies.
   • There is statistically insignificant evidence to conclude that there is a correlation between the number of movies watched per year and the number of books read per year. Thus, the use of the regression line is not appropriate.
   • There is statistically significant evidence to conclude that there is a correlation between the number of movies watched per year and the number of books read per year. Thus, the regression line is useful.
4. r2r2 =  (Round to two decimal places)
5. Interpret r2r2 :
   • There is a large variation in the number books people read each year, but if you only look at people who watch a fixed number of movies each year, this variation on average is reduced by 62%.
   • Given any fixed number of movies watched per year, 62% of the population reads the predicted number of books per year.
   • There is a 62% chance that the regression line will be a good predictor for the number of books people read based on the number of movies they watch each year.
   • 62% of all people watch about the same number of movies as they read books each year.
6. The equation of the linear regression line is:   
   ˆyy^ =   + xx    (Please show your answers to two decimal places)
   
   
   
   
   
7. Use the model to predict the number of books read per year for someone who watches 2 movies per year.
   Books per year =  (Please round your answer to the nearest whole number.)
   
   
   
   
   
8. Interpret the slope of the regression line in the context of the question:
   • For every additional movie that people watch each year, there tends to be an average decrease of 0.76 books read.
   • As x goes up, y goes down.
   • The slope has no practical meaning since people cannot read a negative number of books.
   
   
   
   
   
   
9. Interpret the y-intercept in the context of the question:
   • The average number of books read per year is predicted to be 5 books.
   • The best prediction for a person who doesn't watch any movies is that they will read 5 books each year.
   • The y-intercept has no practical meaning for this study.
   • If someone watches 0 movies per year, then that person will read 5 books this year.

The scenario for this assessment is a multi-specialty hospital system, the Royal Rundle Hospital (RRH), that provides a broad range of services to the community which include surgical, maternity, obstetric care, dialysis, emergency, mental health, aged and palliative care, allied health services and a 24-hour emergency department. The RRH has been serving in the region for over 50 years and has been using paper-based forms and documents to store and manage all the data with some use of spreadsheets that started not so long ago. Now that the management of RRH wants to take the advantages of Information Technology to maintain and manage the records of the various aspects of the hospital system more efficiently, they have put out a Request for Proposals (RFP) for appropriately qualified consultants to undertake a body of work that would help to scope the data requirements for such a system. With your success in your Torrens University Australia degree so far, and other similar projects that have garnered you some sustained success in the eyes of the profession and community, you have been shortlisted among no less than 10 other consultancies. There are expectations from them, then, as to the standard of report you will produce. The management of the RRH has provided you with an overview and description of the hospital system as below Overview: The Royal Rundle Hospital (RRH) is a multi-specialty hospital that includes a number of departments, rooms, doctors, nurses, compounders, and other staff working in the hospital. Patients having different kinds of ailments come to the hospital and get checkup done from the relevant doctors. If required they are admitted in the hospital and discharged after treatment. The hospital maintains the records of various departments, rooms, and doctors in the hospital besides the most important records of the regular patients, patients admitted in the hospital, the checkup of patients done by the doctors, the patients that have been operated, and patients discharged from the hospital. Description: In RRH, there are many departments like Orthopedic, Pathology, Emergency, Dental, Gynecology, Anesthetics, I.C.U., Blood Bank, Operation Theater, Laboratory, M.R.I., Neurology, Cardiology, Cancer Department, Corpse, etc. There is an OPD where patients come and get a card (that is, entry card of the patient) for check up from the relevant doctor. After making entry in the card, they go to the relevant doctor’s room and the doctor checks up their ailments. According to the ailments, the doctor either prescribes medicine or admits the patient in the relevant department. The patient may choose either private or general room according to his/her need. But before getting admission in the hospital, the patient has to fulfill certain formalities of the hospital like room charges, etc. After the treatment is completed, the doctor discharges the patient. Before discharging from the hospital, the patient again has to complete certain formalities of the hospital like balance charges, test charges, operation charges (if any), blood charges, doctors’ charges, etc. Next, the management talks about the doctors of the hospital. There are two types of the doctors in the hospital, namely, regular doctors and call-on doctors. Regular doctors are those doctors who come to the hospital daily. Call-on doctors are those doctors who are called by the hospital if the relevant regular doctor is not available.

TASK:- System Vision Document

A nations population size and the affluence of its citizens each influence its resource consumption and environmental impact. As of 2019, the world’s population passed 7.76 billion, average per capita income was $15,415 per year, and the latest estimate for the worlds average ecological footprint is 2.8 hectares per person. The sampling of data in the table will allow you to explore patterns in how population, affluence, and environmental impact are related.

1. Calculate the total environmental impact (national ecological footprint) for each country. Multiply column 1 (population) by Personal Impact (column 3).`

2. Which Country has the greatest IPAT? Why? Incorporate Population Size, Affluence and Footprint into your answer.

3. Which Country has the lowest IPAT? Why? Incorporate Population Size, Affluence and Footprint into your answer.

4. Compare Belgium and the US -both have the two highest Affluence, which are quite similar ($ 56K vs. $ 44K). The Personal Impact for both countries also is similar (8.2 vs. 7.4, respectively) yet the US has a population roughly 30x larger. In this example, what factor do you think (Affluence, Population size, or Personal Impact) carries the most weight in terms of influencing the Total National Impact/Ecological Footprint.

The molecular orbitals associated with the π-bonding MOs in square cyclobutadiene (C4H4) are, like benzene, form by overlap of a single p-orbital on each carbon atom that is not involved in the sigma-bonding network of the molecule. These p-orbitals point perpendicularly with respect to the plane defined by the carbon atoms. There is no central atom, so the only interactions that matter are between the p-orbitals among themselves.

i) draw the four π-orbitals of C4H4

ii) Use the idea that the energy of a MO increases with number of new nodes made during bonding (i.e. nodes not already present in initial AO functions) to sketch a molecular orbital energy level diagram for the π-molecular orbitals of C4H4. Remember that, by definition, degenerate orbitals are identical except for trivial rotation in space, and have identical energy.

iii) Fill the MOs with the electrons from the atomic p-orbitals that you used to form the π-MOs of C4H4. Use your diagram to determine the overall bond order by considering each doubly occupied bonding MO to contribute 1, each nonbonding orbital 0 and each antibonding orbital -1. The result would be divided by 4 C-C bonds to get the average contribution to each C-C bond from π-bonding, which then should be added to a σ-bonding contribution of 1.0

iv) Repeat step (iii) for the dication C4H4 2+ to determine the net bond order for this species. Why do you think you got this value?

v) Predict which of C4H4 and C4H4 2+ could be observed by ESR spectroscopy

vi) Which of C4H4 2+ and C4H4 is more likely to be susceptible to electrophilic attack.

Just need a basic, but ACCURATE, run through. Will thumbs up. Please and Thank you.

3. A psychologist believed that as children get older, they engage in more “inactive activities” such as playing computer games, watching TV and surfing the internet. She collected data from 10 children. She recorded the age of each child and the amount of activity (in hours) the child engaged in per week. The table below gives the data for this hypothetical study (it is also available in activity.txt). Age (years) Amount of Activity (hours) 7 4.3 9 3.2 10 1.0 13 1.5 12 1.2 15 0.8 9 3.0 12 4.0 15 1.5 14 1.9

a. Using R, obtain a scatterplot of the data. Discuss the relationship between age and activity based on the scatterplot.

b. Using R, obtain the simple linear regression linear regression line predicting activity from age.

c. Interpret the intercept and slope of the regression line

d. By hand, predict the amount of activity for age = 14

e. By hand, calculate the residual for age = 14

f. Using R output, test the null hypothesis that the slope coefficient is zero using the p-value approach. Write one sentence interpreting the meaning of this result. Make sure to report the test statistic and p-value.

g. Using R, obtain and report the 95% CI for the slope coefficient. Explain how we can use it to make a decision about the null hypothesis from part (f).

h. Using R output, test the null hypothesis that the population coefficient of determination is zero using the p-value approach, and write one sentence interpreting your result. Make sure to report the test statistic and p-value.

i. How do the test statistics in (f) and (h) mathematically relate to each other?

Smoky Mountain Corporation makes two types of hiking boots—the Xtreme and the Pathfinder. Data concerning these two product lines appear below: Xtreme Pathfinder Selling price per unit $ 124.00 $ 88.00 Direct materials per unit $ 63.40 $ 53.00 Direct labor per unit $ 14.40 $ 8.00 Direct labor-hours per unit 1.8 DLHs 1.0 DLHs Estimated annual production and sales 23,000 units 70,000 units The company has a traditional costing system in which manufacturing overhead is applied to units based on direct labor-hours. Data concerning manufacturing overhead and direct labor-hours for the upcoming year appear below: Estimated total manufacturing overhead $ 2,005,200 Estimated total direct labor-hours 111,400 DLHs Required: 1. Compute the product margins for the Xtreme and the Pathfinder products under the company’s traditional costing system. 2. The company is considering replacing its traditional costing system with an activity-based costing system that would assign its manufacturing overhead to the following four activity cost pools (the Other cost pool includes organization-sustaining costs and idle capacity costs): Estimated Overhead Cost Expected Activity Activities and Activity Measures Xtreme Pathfinder Total Supporting direct labor (direct labor-hours) $ 712,960 41,400 70,000 111,400 Batch setups (setups) 504,000 230 190 420 Product sustaining (number of products) 740,000 1 1 2 Other 48,240 NA NA NA Total manufacturing overhead cost $ 2,005,200 Compute the product margins for the Xtreme and the Pathfinder products under the activity-based costing system. 3. Prepare a quantitative comparison of the traditional and activity-based cost assignments.

A horticulturist is studying the relationship between tomato plant height and fertilizer amount. Thirty tomato plants grown in similar conditions were subjected to various amounts of fertilizer over a four-month period, and then their heights were measured. The results are shown in the accompanying table. Fertilizer Amount (ounces) Tomato Plant Height (inches) 1.9 20.4 5.0 29.1 4.2 28.2 1.3 24.3 4.9 29.2 5.4 29.8 3.1 34.6 0.0 25.3 2.3 26.2 2.5 25.7 0.9 26.5 1.0 28.6 4.5 25.7 3.8 36.8 5.3 27.2 2.3 33.4 4.0 25.1 1.4 22.1 3.9 40.6 4.0 24.5 3.6 39.7 0.6 21.1 1.6 25.4 2.5 29.6 4.5 27.6 3.6 32.6 2.0 33.5 0.0 22.5 2.5 27.6 3.1 36.4 Picture Click here for the Excel Data File a. Estimate the linear regression model: Height = β0 + β1Fertilizer + ε. (Round your answers to 3 decimal places.) Heightˆ = 25.000 + 1.290 Fertilizer b-1. Estimate the quadratic regression model: Height = β0 + β1Fertilizer + β2Fertilizer2 + ε. (Round your answers to 3 decimal places.) Heightˆ = 21.100 + 5.460 Fertilizer + 0.759 Fertilizer2 b-2. Using the quadratic results, find the fertilizer amount at which the height reaches a minimum or maximum. (Round your intermediate values and final answer to 3 decimal places.) Fertilizer amount = 3.9 ounces c. Use the best-fitting model to predict, after a four-month period, the height of a tomato plant that received 3.0 ounces of fertilizer. (Round your intermediate values and final answer to 2 decimal places.) Heightˆ = 30.649 inches

Smoky Mountain Corporation makes two types of hiking boots—the Xtreme and the Pathfinder. Data concerning these two product lines appear below:

The company has a traditional costing system in which manufacturing overhead is applied to units based on direct labor-hours. Data concerning manufacturing overhead and direct labor-hours for the upcoming year appear below:

Required:

1. Compute the product margins for the Xtreme and the Pathfinder products under the company’s traditional costing system.

2. The company is considering replacing its traditional costing system with an activity-based costing system that would assign its manufacturing overhead to the following four activity cost pools (the Other cost pool includes organization-sustaining costs and idle capacity costs):

Compute the product margins for the Xtreme and the Pathfinder products under the activity-based costing system.

3. Prepare a quantitative comparison of the traditional and activity-based cost assignments.

Assume that you recently graduated and you just landed a job as a financial planner with the Cleveland Clinic. Your first assignment is to invest $100,000. Because the funds are to be invested at the end of one year, you have been instructed to plan for a one-year holding period. Further, your boss has restricted you to the following investment alternatives, shown with their probabilities and associated outcomes.          

Barney Smith Investment Advisors recently issued estimates for the state of the economy and the rate of return on each state of the economy. Alta Industries, Inc. is an electronics firm; Repo Men Inc. collects past due debts; and American Foam manufactures mattresses and various other foam products. Barney Smith also maintains an "index fund" which owns a market-weighted fraction of all publicly traded stocks; you can invest in that fund and thus obtain average stock market results. Given the situation as described, answer the following questions.

Suppose you create a two-stock portfolio by investing $50,000 in Alta Industries and $50,000 in Repo Men. Calculate the expected return, standard deviation, coefficient of variation, and beta for this portfolio. How does the risk of this two-stock portfolio compare with the risk of the individual stocks if they were held in isolation? **Please show all calculations and formulas used to derive the answers**