The following table shows age distribution and location of a random sample of 166 buffalo in a national park.

Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: Age distribution and location are not independent.
H₁: Age distribution and location are not independent.H₀: Age distribution and location are independent.
H₁: Age distribution and location are not independent.    H₀: Age distribution and location are not independent.
H₁: Age distribution and location are independent.H₀: Age distribution and location are independent.
H₁: Age distribution and location are independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

YesNo    

What sampling distribution will you use?

Student's tbinomial    normalchi-squareuniform

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

p-value > 0.1000.050 < p-value < 0.100    0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is sufficient evidence to conclude that age distribution and location are not independent.At the 5% level of significance, there is insufficient evidence to conclude that age distribution and location are not independent.    

1.A- The government of River City, population 750,000, wants to know how best to allocate funds to serve its residents. Right now it is trying to determine whether to continue funding the "Concerts in the Park" summer music series. To gather data, it hires a firm that specializes in marketing research via telephone. The firm makes 200 calls asking respondents how often they attend the shows.

The size of the sample in question here is relatively (large/small) and the data (are/are not) likely to have significant outliers or large gaps in the values.

What is the best measure of centrality to use in this case? A-Mean ; B-median; C-Weighted mean ;D-Mode

1.B-Otis needs to know how many people his elevators can carry safely. He already knows how much weight they can bear before malfunctioning, so he needs to divide that by the average weight of a person. He uses a large pool of data from the federal government to calculate that average, which he then uses to estimate the largest group of people his elevators will safely accommodate.

The size of the sample in question here is relatively (large/small), and the data(are/are not) likely to have significant outliers or large gaps in the values.

What is the best measure of centrality to use in this case? A-Mean ; B-median; C-Weighted mean ;D-Mode

1.C-The Bakunin Banking Corp. employs 32 people. Upper management includes the CEO, who makes about $1.2 million per year with bonuses; the CFO, who earns $850,000; and three department heads, who each make between $700,000 and $750,000. The company also has two IT staff members, who each make $80,000. The rest of the employees work as clerks and earn between $20,000 and $27,000 dollars. The clerks are thinking about unionizing, and in making their case, they want to emphasize the disparate incomes at the firm.

The size of the sample in question here is relatively (large/small), and the data(are/are not) likely to have significant outliers or large gaps in the values.

What is the best measure of centrality to use in this case? A-Mean ; B-median; C-Weighted mean ;D-Mode

Three years ago, Vincent Chow completed his college degree. The economy was in a depressed

state at the time, and Vincent managed to get an offer of only $25,000 per year as a bookkeeper. In

addition to its relatively low pay, this job had limited advancement potential. Since Vincent was an

enterprising and ambitious young man, he instead started a business of his own. He was convinced

that because of changing lifestyles, a drive-through coffee establishment would be profitable. He

was able to obtain backing from his parents to open such an establishment close to the industrial

park area in town. Vincent named his business The Cappuccino Express and decided to sell only

two types of coffee: cappuccino and decaffeinated.

As Vincent had expected, The Cappuccino Express was very well received. Within three

years, Vincent had added another outlet north of town. He left the day-to-day management of each

site to a manager and turned his attention toward overseeing the entire enterprise. He also hired an

assistant to do the record keeping and other selected chores.

REQUIRED

a. Develop an organization chart for The Cappuccino Express.

b. What factors can be expected to have a major impact on the success of The Cappuccino

Express?

c. What major tasks must Vincent undertake in managing The Cappuccino Express?

d. What are the major costs of operating The Cappuccino Express?

e. Vincent would like to monitor the performance of each site manager. What measure(s) of

performance should he use?

f. If you suggested more than one measure, which of these should Vincent select if he could use

only one?

g. Suppose that last year, the original site had yielded total revenues of $146,000, total costs

of $122,000, and hence, a profit of $24,000. Vincent had judged this profit performance to

be satisfactory. For the coming year, Vincent expects that due to factors such as increased

name recognition and demographic changes, the total revenues will increase by 20 percent to

$175,200. What amount of profit should he expect from the site? Discuss the issues involved

in developing an estimate of profit.

Please read the case study entitled “Casinos and Crime” that you find in the reading assignment. Based on what you have learned in this unit, answer the following questions: 1. In most casino states and counties, laws protect owners from liability claims arising from problems caused by gambling. In ethical terms, however, if you’re the sole proprietor of the casino, do you feel any responsibility for this episode? Why or why not? If you feel any responsibility, to whom would it be? What could you do to set things right? 2. You’re an equal partner in a nonprofit organization that runs the casino to support the cause of building schools for children in impoverished sections of Peru. You spend a few months every year down there building schools and giving free English-language classes. In ethical terms (and regardless of what the law allows), do you believe anyone involved in this episode should be able to sue you personally for their suffering? Why or why not? 3. Say that the casino under discussion in this set of questions is the MGM Grand Hotel and Casino in Las Vegas, which is owned by a large, public corporation. You have five shares of stock inherited a few years ago when a relative died. You are legally protected from liability claims. In ethical terms, however, do you believe that anyone involved in this episode should be able to sue you personally—or just plain blame you—for their suffering? Why or why not? 4. Pigouvian taxes (named after economist Arthur Pigou, a pioneer in the theory of externalities) attempt to correct externalities—and so formalize a corporate social responsibility—by levying a tax equal to the costs of the externality to society. The casino, in other words, that causes crime and other problems costing society, say, $1 million should pay a $1 million tax. In terms of casinos, would such a tax more or less satisfy any ethical claim that could be made against them for the social problems they cause? Why or why not? https://2012books.lardbucket.org/books/business-ethics/s17-05-case-studies.html

​​​​​​The following table shows age distribution and location of a random sample of 166 buffalo in a national park.

Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: Age distribution and location are not independent.
H₁: Age distribution and location are not independent.H₀: Age distribution and location are independent.
H₁: Age distribution and location are independent.    H₀: Age distribution and location are not independent.
H₁: Age distribution and location are independent.H₀: Age distribution and location are independent.
H₁: Age distribution and location are not independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

YesNo    

What sampling distribution will you use?

uniformchi-square    normalStudent's tbinomial

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

p-value > 0.1000.050 < p-value < 0.100    0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is sufficient evidence to conclude that age distribution and location are not independent.At the 5% level of significance, there is insufficient evidence to conclude that age distribution and location are not independent.    

1. Net Present Value (NPV) and Internal Rate of Return (IRR) (question)

The City and County of Denver is completing a $45 million renovation of City Park Golf Course. To complete the renovation, the course has been closed to the public for 2.5 years (planned re-opening is Spring 2020). The project updated the course, built a new clubhouse that can accommodate golf and community events, resulted in a “net gain of 500 trees”, and reduced flood risk “for thousands of homes”.[1] All of these updates are expected to provide either increased revenue or reduced costs. Assume the $45 million cost was paid upfront by Denver and the following are the estimated cash receipts and disbursements associated with the project.[1] If the cost of capital is 6%, does the project make sense based on NPV and IRR over a 30-year useful life? Does your finding change if the cost of capital is actually 4%?

[

Suppose you work for an insurance company. You know that there are equal numbers of individuals who will get in an accident with probability 0.2 and 0.3 and that the loss from getting in an accident is $4,000. Suppose you wish to screen individuals by offering full- coverage insurance as well as 30 percent coinsurance (i.e., the insurance pays 30 percent of the loss amount, or $1,200, in the event of an accident). You wish to include a 5 percent premium over the actuarially fair values for these policies to help cover overhead and pro- vide a profit margin for your company.

Will this pair of policies screen individuals into risk classes if we assume that all insuredindividuals have utility function U(X) ? 2000 · (X/4000)0.5 where X is income? Hint: Calculate utility (or expected utility) for each of the three options (no insurance, full- coverage insurance, and coinsurance) for both types of individuals and compare ex- pected utility levels to see what each will choose.

Background on Expected Utility: In this conceptualization of utility, we can compare uncertain outcomes with certain outcomes. For example, if an individual does not have insurance and does not get into an accident, he or she has a utility level of 2,000 (because X ? $4,000) or zero if he or she gets into an accident (because then X ? $0). The expected utility (EU) is based on the likelihood of each event occurring. A per- son facing a 10 percent chance of having an accident would have an expected utility of 1,800 using this utility function because EU ? 0.9 · 2,000 ? 0.1 · 0. This person would be indifferent between facing this “lottery” and having $3,240 with certainty (because U(3240) ? 1,800). This certainty equivalent value was obtained by solving for X in the equation 1800 ? 2000 · (X/4000)0.5. The lottery would be preferred to amounts less than $3,240 offered with certainty.