Two towns, each with three members are deciding whether to put on a fireworks display to celebrate the New Year. Fireworks cost $360. In each town, some people enjoy fireworks more than others.

a.In the town of Bayport, each of the residents value the public good as follows:Frank$50Joe$100Caline $300Would fireworks pass a cost-benefit analysis?

Explain.

b.The mayor of Bayport proposes to decide by majority rule and , if the fireworks referendum passes, to split the cost equally among all the residents. Who would vote in favor, and who would vote against? Would the vote yield the same answer as the cost-benefit analysis?

c.In the town of River Heights, each of the residents values the public good as follows:

Nancy $20

Bess$140

Ned$160

Would fireworks pass a cost-benefit analysis? Explain.

d.The mayor of River Heights also proposes to decide by majority rule and, if the fireworksreferendum passes, to split the cost equally among all residents. Who would vote in favor,and who would vote against? Would the vote yield the same answer as the cost-benefit analysis?

e.What do you think these examples say about the optimal provision of public goods?

The local bank pays 4% interest on savings deposits. In a nearby town, the bank pays 1% per quarter. A man who has $2945 to deposit wonders whether the higher interest paid in the nearby town justifies driving there. If all money is left in the account for 3 years, how much more money would he obtain if the out-of-town bank was chosen?

The local bank pays 5% interest on savings deposits. In a nearby town, the bank pays 1.25% per quarter. A man who has $4000 to deposit wonders whether the higher interest paid in the nearby town justifies driving there. If all money is left in the account for 3 years, how much interest would he obtain from the out-of-town bank?

With a town of 20 people, 2 have a certain disease that spreads as follows: Contacts between two members of the town occurred in accordance with a Poisson process having rate ?. When contact occurs, it is equally likely to involve any of the possible pairs of people in the town. If a diseased and non-diseased person interect, then, with probability p the non-diseased person becomes diseased. Once infected, a person remains infected throughout. Let ?(?) denote the number of diseased people of the town at time t. Considering the current time as t = 0, we want to model this process as a continuous-time Markov chain.

(a) What is the state space of this process?

(b) What is the probability that a diseased person contacts a non-diseased person?

(c) What is the rate at which a diseased person contacts a non-diseased person (we denoted this type of contact by I-N contact) when there are X diseased people in the town?

(d) Is the inter-contact time between two I-N contacts exponentially distributed? Why?

(e) Compute the expected time until all people of the town are infected by the disease.

For a weekly town council meeting in a certain town, the distribution of the duration of the meeting is approximately normal with mean 53 minutes and standard deviation 2.5 minutes. For a weekly arts council meeting in the same town, the distribution of the duration of the meeting is approximately normal with mean 56 minutes and standard deviation 5.1 minutes. Let x¯1 represent the average duration, in minutes, of 10 randomly selected town council meetings, and let x¯2 represent the average duration, in minutes, of 10 randomly selected arts council meetings. Which of the following is the best reason why the sampling distribution of x¯1−x¯2 can be modeled by a normal distribution? The sample sizes are equal.

A Both sample sizes are large enough to satisfy the normality condition.

B The population distributions are approximately normal.

C The population standard deviations are assumed equal.

D The sample sizes are less than 10% of the corresponding population sizes.

Recipes for the same type of cookies can vary in terms of ingredients and baking times. From a collection of chocolate chip cookie recipes, a baker randomly selected 5 recipes. From a collection of oatmeal raisin cookie recipes, the baker randomly selected 4 recipes. The mean baking times, in minutes, for each sample were recorded as x¯C and x¯O, respectively. What is the correct unit of measure for the standard deviation of the sampling distribution of x¯C−x¯O?

A Minutes

B Minutes squared

C Recipes

D Number of Raisins

E Number of Chocolate Chips

A Bacon Factory is located in a small town. Also in the town is a Water Park. The smell of the Bacon factory has adversely affected the Water Park such that it has put in air cleaning equipment to eradicate the odor created by the factory.

The cost function of the Bacon Factory is: CBF= B² + 4B^1/2 + (1 − x)²

where B denotes the quantity of bacon produced annually and x denotes the quantity of pollutants that A creates in a given year.

Thus, the Bacon Factory can limit production costs by eliminating its air scrubbers. However, the air pollution increases the costs for the water park W, whose cost function is: C_WP = W² + 2x where W denotes the number of visitors to the Water Park on an annual basis. Suppose that the unit price of admission to the water park is $3 and that the unit price of bacon is $32.5 per unit.

1. Compute the profit maximizing visits (represented by W) created by Firm W (assuming W behaves competitively in the output market). Notice that W does not choose x. Also, compute W’s profits.

2. Suppose now that the two firms B and W merge, creating B&W. The management of B&W now maximizes B&W’s profits by appropriately choosing x, B, and W. Find the quantities of Bacon, Water Park Visits, and pollutants that the new firm produces. Also, find the profits of B&W.

A Bacon Factory is located in a small town. Also in the town is a Water Park. The smell of the Bacon factory has adversely affected the Water Park such that it has put in air cleaning equipment to eradicate the odor created by the factory. Please show your work..

The cost function of the Bacon Factory is:

      C_BF= B² + 4B^1/2 + (1 − x)²

where B denotes the quantity of bacon produced annually and x denotes the quantity of pollutants that A creates in a given year.

Thus, the Bacon Factory can limit production costs by eliminating its air scrubbers. However, the air pollution increases the costs for the water park W, whose cost function is:

      C_WP = W² + 2x,

where W denotes the number of visitors to the Water Park on an annual basis.   Suppose that the unit price of admission to the water park is $3 and that the unit price of bacon is $32.5 per unit.

A. Compute the profit maximizing quantity of the Bacon Factory (B) and pollutant (x) produced by Bacon Factory B (assuming B behaves competitively in the output market, i.e., taking the price of Bacon as $32.50). Also, compute the Bacon Factory’s (Firm B) profits.

B. Compute the profit maximizing visits (represented by W) created by Firm W (assuming W behaves competitively in the output market, i.e., taking the price of visits as given). Notice that W does not choose x. Also, compute W’s profits.

C . Suppose now that the two firms B and W merge, creating B&W. The management of B&W now maximizes B&W’s profits by appropriately choosing x, B, and W. Find the quantities of Bacon, Water Park Visits, and pollutants that the new firm produces. Also, find the profits of B&W.

The mayor of a small town claims that in his town there is no significant difference between the proportion of male and female (between the ages of 21 and 65) that have jobs. To test this claim, a statistician randomly sampled 30 male and 40 female residents and found that 25 males and 25 females have jobs.

a. What are p^1and p^2? [ Sample answer: "phat1 = 0.262 ; phat2 = 0.635"]

b. What is the Point Estimate for (p1−p2)?

c. What is the Margin of Error at 90% confidence level?

d. What is the Confidence Interval (CI)? [Sample answer: "0.145 < p1 - p2 < 0.258"]

e. From the CI in part (d), can the mayor’s claim be justified? Explain.

To increase attendance, the marketing department for a major league baseball team targeted advertising toward families, children, and females in order to attract more attendees. Past figures showed an average per game of 58% male (age 12 and over), 28% female (age 12 and over), and 14% children (under 12). Therefore, in the past, an average per game of 42% were female or children and the goal of the advertising was to improve that percentage. After two months of advertising, the marketing director reported an average per game of 54% of the attendees were either females or children under 12.

1) Observe the statistics below and either verify or dispute the director's claim. Include in your work the answer to the following question: If a fan is randomly selected, what is the probability of selecting a woman or a child under 12? Show, in detail.

2) How large would you say the increase in the number of females and children under 12 must be in order to say that the advertising worked? Does any increase indicate improvement, or would there have to be a significant amount? If a significant amount, what would you consider a significant amount in this case?

All attendees Average per game over the past two months (all ages):

Males (all) 19,600

Females (all) 10,400

Total 30,000

Children under 12 Average per game over the past two months:

Boys (under 12) 3,100

Girls (under 12) 2,700

Total 5,800

In what ways and why have women and girl offenders traditionally been treated differently from men and boys in the criminal justice system?