In our lecture on Planning Ahead: Sampling variability, you were introduced to a set of five (5) questions that can be used to help decide upon a relevant statistical inference procedure.

1. Identify each of the five (5) questions and answer each question based on the scenario described above.
2. Based on your answers to part a, identify which of the inference procedures covered in class is most appropriate to analyse the researcher’s data?
3. Assume the researchers for the above scenario have obtained relevant simple random sample(s). Identify (by name) the sampling distribution that underlies the statistical inference procedure named in part b. Then, give the formulae for the mean and standard deviation for the sampling distribution you have identified.

my answer to a is:

1. The first question is “what is your analysis goal?”. The analysis goal based on the scenario above is to determine if student employment has an influence on their academic success. The second question is “how many ‘samples’ or groups are you comparing?”. Based on the scenario above, the researcher is comparing a single sample of university students and each student in the sample is surveyed. The third question is “are you ‘samples’ independent or paired?”. In this scenario, the sample is independent as the data is obtained from each student each case is unrelated to the other. The fourth question is “what type of data are you collecting? Quantitative or categorical?”. Based on the scenario above, the data being collected quantitative. Both the employment status and their course grades produce a numerical value to describe the dat The last question is “what parameters are of interest?”. In the above scenario, the parameters of interest are the hours worked per week and the mean of the student’s course grades.

Janet and Paul have been married for 17 years. They have 3 children, Susan, age 16, Jonathan, age 14, and Lillian, age 6. Janet abuses alcohol and as a result has been neglectful of the children’s care and emotional needs. Paul is in the military and spends a lot of time away and is thus unaware of Janet’s problem and how it is affecting the children. When Paul is around, he is quite strict with the children, which confuses them since Janet is so unstructured. Paul and Janet have had some conflicts as a couple throughout the years, and sought counseling some years ago, At the time, Janet was drinking but not as heavily as she is now. Janet has a history of depression and has taken antidepressant medication at times. Janet’s mother was also an alcoholic and suffered from depression. When Janet is not drinking, she appears to be overly strict, impulsive, apathetic and lacking in self-esteem.

Susan, the oldest child, is highly mature and responsible, and seems to do most of Lillian and Jonathan’s care when her mother is unavailable. Susan feels embarrassed about her mother’s alcohol problem and tries to keep this a secret. At times, she just stays late at the library to avoid having to face her mother and focuses on school as a way to distract herself from the problem. Lately her sense of responsibility has made her feel guilty about not being home to protect her siblings since her mother’s behavior has worsened.

Jonathan has been quite aggressive in school lately, too. The teacher has noticed that he fluctuates between anger and silent withdrawal. Lillian’s teacher has noticed the child’s need for attention and wonders if she is being neglected at home. Lillian is often shy, lonely and withdrawn. The teacher has invited Lillian’s parents for a conference but has not received a response. The teacher referred Lillian to the school counselor who, after noticing a couple of bruises on Lillian, was suspicious of abuse and called child protective services. Following an investigation, the family has been referred to mandatory family counseling, a parenting skills program, and alcohol treatment for Janet.

Clinical Activity:

As a family therapist what position would you take with this family?

Peter is a twenty-year-old Caucasian college student referred for counseling by the dean of academic affairs. Peter has been suspended from school for drinking and fighting on two occasions over the past six weeks. He has a history of recurrent detentions and classroom dismissals for similar, though less severe, behavior since high school. Peter was suspended for having a pint of vodka and a small quantity of marijuana in his locker. Peter has recently started experiencing mood swings and is feeling depressed and agitated. Earlier, having felt that the stress of home life was the root cause of his depression, Peter thought that leaving home and living on-campus would resolve his mood swings. He has been practicing self-medication with marijuana and alcohol. He disclosed that he had been prescribed medication for depression when he was in high school but has since then stopped all medication and follow-up on mental health counseling. Presently, he has no desire to enter or seek treatment voluntarily. He has come in for therapy only to avoid being expelled from the college. He denies having any problem with either alcohol or drugs and feels marijuana should be legalized. In addition, he compares his alcohol and drug use to others' and does not think his intake of substances is a problem. He feels that everyone is just picking on him; he works hard and should be allowed to do. He takes alcohol or marijuana because he just wants to relax after a tough day's work. Based on your understanding of the above scenario and drawing upon all relevant course material, address the following questions: Does Peter have a co-occurring mental disorder? Describe what that disorder may be based on the symptoms mentioned in the case scenario.Analyze and justify the co-occurring disorders in the case. At what stage of change does Peter appear to be in? Why? Explain. What model of treatment could possibly work with Peter? Would he do well with a psycho-educational model, CBT, behavioral approach? Why? Share your clinical recommendations based on research. What are the relapse concerns? Are there any noted defense mechanisms intact?

Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

1. 1) The probability that an employee at a company eats lunch at the company cafeteria is 1) 0.32. The probability that an employee is female is 0.62. The probability than an
   employee eats lunch at the employee cafeteria and is female is 0.21. What is the
   probability that a randomly chosen employee either eats at the cafeteria or is female?

2. 2) In a recent article it was reported that 27.3% of all college students party during 2) weekdays, and 67% of these students plan on going to graduate school. What is the probability that a randomly-selected student party during weekdays and plans on
   going to graduate school?

3. 3) There are five men and four women working on a project. To handle one particular 3) aspect of the project, a subcommittee needs to be formed. In the interest of balance, it is decided that the subcommittee will consist of two men and two women. How many combinations of this subcommittee are possible?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A student has access to professor evaluations. Overall, he has enjoyed 70% of all classes he has taken. He finds that of the courses he has enjoyed, 13% were taught by professors with poor evaluations. 84% of the courses he has taken were taught by professors with good evaluations.

4) What is the probability that the class was taught by a professor with good evaluations 4) and that the student enjoyed the class?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
In a recent survey about US policy in Iraq, 62 % of the respondents said that they support US policy in Iraq. Females comprised 53% of the sample, and of the females, 46% supported US policy in Iraq. A person is selected at random.

5. 5) What is the probability that the person we select is female and supports U.S. policy in 5) Iraq?

6. 6) Are the events "does not support U.S, policy in Iraq" and "female" statistically 6) independent? Why or why not?

7. 7) Suppose we select a supporter of US policy in Iraq, what is the probability that the 7) person we select is female?

8. 8) Suppose we select a person who does not support US policy in Iraq, what is the 8) probability that the person is male?

1

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
James' Surfboard Shop makes surfboards by hand. The number of surfboards that James makes during a week depends on the wave conditions. James has estimated the following probabilities for surfboard production for the next week.

Number of Surfboards 5 6 7 8 9 10 Probability 0.13 0.22 0.31 0.17 0.13 0.04

Let A be the event that James produces more than seven surfboards. Let B be the event that James produces exactly six surfboards.

9. 9) What is the probability of event A? 9)

10. 10) What is the probability of the complement of A? 10)

11. 11) What is the probability of the intersection of events A and B ? Why? 11)

12. 12) Are events A and B collectively exhaustive? Why? 12)

13. 13) The probability that a new small business closes before the end of its first year is 42%. 13) In addition, 37% of all new businesses are started by women. The probability that a
    new business is either owned by a woman or goes out of business is 62%. Your sister
    starts a new business. What is the probability her business will still open at the end of

    the first year?

14. 14) In a survey of top executives, it was found that 17% had traveled internationally 14) on business. The probability of one of these executives fluently speaking a foreign
    language was found to be 10%. The probability that one of these executives neither
    spoke a foreign language nor had traveled internationally was 0.81. What is the

    probability that an executive who speaks a foreign language has traveled internationally?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Consider a sample space defined by events A1, A2, B 1, B2. Let P (A1) = 0.40 , P (B 1 ! A1) = 0.60 and P (B 1 ! A2) = 0.70

15) What is P(A2)?
16) What is P(A1 "B1)? 17) What is P(A1 "B2)? 18) What is P(A2 "B1)?

15) 16) 17) 18)

Thanks, please show all work!

Statistical Methods of Business I – Case Study

Texas is home to more than one million undocumented immigrants, and most of them are stuck in low-paying jobs. Meanwhile, the state also suffers from a lack of skilled workers. The Texas Workforce Commission estimates that 133,000 jobs are currently unfilled, many because employers cannot find qualified applicants (The Boston Globe, September 29, 2011). Texas was the first state to pass a law that allows children of undocumented immigrants to pay in-state college tuition rates if they have lived in Texas for three years and plan to become permanent residents. The law passed easily back in 2001 because most legislators believed that producing college graduates and keeping them in Texas benefits the business community. In addition, since college graduates earn more money, they also provide the state with more revenue.

Chuck Norris, who sits on the Board of Directors for the Texas Workforce Commission suggests the board should hire your consulting firm, Stat Solutions, to estimate the mean hourly wage of workers with various levels of education. You accept the job and a sample is collected of the hourly wages of 30 Texas workers with a bachelor’s degree or higher, 30 Texas workers with only a high school diploma, and 30 Texas workers who did not finish high school.

Chuck wants you to provide a full report for him to present at the next meeting of the Texas Workforce Commission Board of Directors which occurs in 10 days.

Requirements and associated point values:

Part 1 – Calculate and use descriptive statistics to compare hourly wages for each of the education levels. Be sure to include the mean, standard deviation and margin of error with 95% confidence for each of the 3 levels (9 calculations). These calculations range in value from 3-4 points each for a total of 33 points. Note: See page 293 for the margin of error formula.

Part 2 – Construct and interpret 95% confidence intervals for the mean hourly wage at each education level. There should be an upper and lower number for each of the 3 levels. The end result should be 6 numbers which are valued at 3 points each for a total of 18 points.

1. Refer to the Campus Crime dataset in the EXCEL file. This data comes from a study of 20 campuses selected at random from a list of four-year schools in the continental U.S. Variables include:

• Number of Crimes reported during the most recent reporting year.
• Number of Police on the school’s police force during the most recent reporting year.
• Total Enrollment at the school during the most recent reporting year.
• Total Expenditure ($) on police protection by the school during the most recent reporting year.
• An indicator of whether the school is public or private (1 = Private, 0 = Public)

Further information that may be relevant is that there are 629 public and 1845 private four year institutions in the continental US, enrolling 6.838 million and 4.162 million, respectively during the most recent reporting year.

1. (For part A, assume that you only have columns A and E in the dataset). In an appropriate way, report an interval estimate of the total number of crimes on 4-year college campuses across the U.S. during the most recent reporting year. Briefly also discuss why your method is appropriate.
2. (For part B, you should use any part of the data you determine to be relevant). In an appropriate way, report an interval estimate of the total number of crimes on 4-year college campuses across the U.S. during the most recent reporting year. Briefly also discuss why your method is more appropriate than the method you used in (a).
3. Compare and contrast your estimates from (a) and (b). Identify the differences and explain why the estimates are different.
4. (For part D, again use any part of the data you deem relevant). Estimate the protection cost per police officer for all 4-year colleges across the nation. Briefly also discuss why your method is appropriate.
5. (For part E, again use any part of the data you deem relevant). Estimate the protection cost per enrolled student for all 4-year colleges across the nation. Briefly also discuss why your method is appropriate.

THE MBA DECISION Ben Bates graduated from college six years ago with a finance undergraduate degree. Since graduation, he has been employed in the finance department at East Coast Yachts. Although he is satisfied with his current job, his goal is to become an investment banker. He feels that an MBA degree would allow him to achieve this goal. After examining schools, he has narrowed his choice to either Wilton University or Mount Perry College. Although internships are encouraged by both schools, to get class credit for the internship, no salary can be paid. Other than internships, neither school will allow its students to work while enrolled in its MBA program. Ben’s annual salary at East Coast Yachts is $61,000 per year, and his salary is expected to increase at 3 percent per year until retirement. He is currently 28 years old and expects to work for 40 more years. His current job includes a fully paid health insurance plan, and his current average tax rate is 25 percent. Ben has a savings account with enough money to cover the entire cost of his MBA program. The Ritter College of Business at Wilton University is one of the top MBA programs in the country. The MBA degree requires two years of full-time enrollment at the university. The annual tuition is $65,000, payable at the beginning of each school year. Books and other supplies are estimated to cost $2,800 per year. Ben expects that after graduation from Wilton, he will receive a job offer for about $107,000 per year, with an $20,000 signing bonus. The salary at this job will increase at 4 percent per year. Because of the higher salary, his average income tax rate will increase to 30 percent. The Bradley School of Business at Mount Perry College began its MBA program 16 years ago. The Bradley School is smaller and less well known than the Ritter College. Bradley offers an accelerated, one-year program, with a tuition cost of $78,000 to be paid upon matriculation. Books and other supplies for the program are expected to cost $4,000. Ben thinks that after graduation from Mount Perry, he will receive an offer of $90,000 per year, with a $17,000 signing bonus. The salary at this job will increase at 3.5 percent per year. His average income tax rate at this level of income will be 28 percent. Both schools offer a health insurance plan that will cost $3,500 per year, payable at the beginning of the year. Ben also estimates that room and board expenses will cost $2,500 more per year at both schools than his current expenses, payable at the beginning of each year. The appropriate discount rate is 6.2 percent. Assume all salaries are paid at the end of each year.

Salary Wilton MBA Mount Perry MBA Timeline Timeline Timeline Year Value Year Value Year Value

Davis Uniform Corporation operates a store that sells uniforms. The following are the transactions that occurred during the first quarter of operation- Jan. 1 to Mar. 31, 2021.

Jan.     1   Davis issues 20,000 shares of $1 par value common stock with an issuing price of $10

                 per share.

Jan.     2   Purchased furniture and fixtures from Acme Furniture for $14,400 cash.

Jan.     4   Purchased $1,600 of office supplies for cash.

Jan.   15   Paid $36,000 in advance for one year’s rent on the store building. The rent begins with

                Jan 15. The company counts January for half a month.

Jan.   31   Paid salaries to employees for the first month, $3,600.

Feb.    1    Purchased $62,400 of uniforms inventory on account from the Birdwell Uniforms

                 Manufacturing Company.

Feb.    1    Borrowed $66,000 from a local bank and signed two notes. The first note of                  

                $21,000 requires payment of principal in six months with annual interest rate at 4%.

                The second note of $45,000 requires the payment of principal in two years and annual

                 interest payment with annual interest rate at 5%.

Feb.    6    Sold uniforms on account to St. Jude’s School for $7,200. Cost of the uniforms sold

                 is $4,800.

Feb.    9    Paid Birdwell Uniforms Manufacturing Company $50,000 for the purchase on Feb. 1.

Feb. 20    Sold uniforms to a chemical factory for $79,200 cash. Cost of the uniforms sold is

                 $47,520.

Feb. 23    Purchased $10,000 of uniforms inventory on account from the Birdwell Uniforms

                 Manufacturing Company.

Feb. 28    Paid salaries to employees for the month of February, $4,200.

Mar.   1   Sold uniforms to the football team of Robert Lee High School, and accepted a $12,000,

                three-month, note receivable with annual interest rate at 5%. Cost of the uniforms

                 sold is $9,600.

Mar.   1   Subleased a portion of the building to a jewelry store. Received $3,000 in advance

                 for three months’ rent beginning on Mar. 1.

Mar.   3   Some uniforms were returned by the chemical factory which made a purchase on

                Feb. 20. The selling price and cost of the returned uniforms is $7,200 and 4,320,

                 respectively. Cash of $7,200 is refunded to the customer.

Mar. 23   Paid Birdwell Uniforms Manufacturing Company $14,400 for the purchases in Feb.

Mar. 25   Received $5,800 cash from St. Jude’s School.

Mar. 30   The corporation announced and paid its shareholders cash dividends of $2,500.

Requirements:

1. Analyze the transactions and record journal entries in General Journal.

2. Open accounts in General Ledger and post from the General Journal to the general ledger accounts.

3. Record adjusting entries in General Journal and post to the general ledger accounts.

Additional information:

1. At the end of March, $900 of supplies remained.

2. The furniture and fixtures have a useful life of six years and will be worthless at the end of their useful life.

3.    Salaries for the month of March are $4,600, and will be paid in April.

4.    The company’s management estimated that of the $1,400 remaining on account from St.

             Jude’s School, $200 would be uncollectible.

5.    Income tax rate applied to the company is 21%.

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

Ben Bates graduated from college six years ago with a finance undergraduate degree. Although he is satisfied with his current job, his goal is to become an investment banker. He feels that an MBA degree would allow him to achieve this goal. After examining schools, he has narrowed his choice to either Wilton University or Mount Perry College. Although internships are encouraged by both schools, to get class credit for the internship, no salary can be paid. Other than internships, neither school will allow its students to work while enrolled in its MBA program. Ben currently works at the money management firm of Dewey and Louis. His annual salary at the firm is $65,000 per year, and his salary is expected to increase at 3 percent per year until retirement. He is currently 28 years old and expects to work for 40 more years. His current job includes a fully paid health insurance plan, and his current average tax rate is 26 percent. Ben has a savings account with enough money to cover the entire cost of his MBA program. The Ritter College of Business at Wilton University is one of the top MBA programs in the country. The MBA degree requires two years of full-time enrollment at the university. The annual tuition is $70,000, payable at the beginning of each school year. Books and other supplies are estimated to cost $3,000 per year. Ben expects that after graduation from Wilton, he will receive a job offer for about $110,000 per year, with a $20,000 signing bonus. The salary at this job will increase at 4 percent per year. Because of the higher salary, his average income tax rate will increase to 31 percent. The Bradley School of Business at Mount Perry College began its MBA program 16 years ago. The Bradley School is smaller and less well known than the Ritter College. Bradley offers an accelerated, one-year program, with a tuition cost of $85,000 to be paid upon matriculation. Books and other supplies for the program are expected to cost $4,500. Ben thinks that he will receive an offer of $92,000 per year upon graduation, with an $18,000 signing bonus. The salary at this job will increase at 3.5 percent per year. His average tax rate at this level of income will be 29 percent. Both schools offer a health insurance plan that will cost $3,000 per year, payable at the beginning of the year. Ben also estimates that room and board expenses will cost $2,000 more per year at both schools than his current expenses, payable at the beginning of each year. The appropriate discount rate is 6.3 percent.

Please answer:

current salary______

years until retirement_____

salary increase______

tax rate____

Wilton

tuition per year____

books & supplies____

starting salary____

signing bonus____

salary increase_____

tax rate_____

Mount Perry

tuition per year____

books & supplies____

starting salary____

signing bonus____

salary increase_____

tax rate_____

Both schools

health insurance______

room & board_______

discount rate______