Chapter 6 #5- a, b, c, d

Do towns in Massachusetts with higher elevations tend to get more snowfall? To answer this question, a random sample of five towns in Massachusetts, their average yearly snowfall (in inches), and elevation (in feet) were recorded in Table 6.9.

a) Draw a scatterplot and find the equation for the line of best fit.

b) Find the residual for Springfield.

c) Interpret whether or not you believe there is a significant relationship between the average snowfall and elevation in Massachusetts.

d) Find and interpret a 95% confidence interval for the true population slope parameter.

the Elements of Style, read the following excerpts -- both from the same author, George Orwell, and explain the different stylistic forms he uses in each.

Excerpt from 1984

Power is not a means; it is an end. One does not establish a dictatorship in order to safeguard a revolution; one makes the revolution in order to establish the dictatorship. The object of persecution is persecution. The object of torture is torture. The object of power is power.

Excerpt from "Shooting an Elephant"

In Moulmein, in lower Burma, I was hated by large numbers of people – the only time in my life that I have been important enough for this to happen to me. I was sub-divisional police officer of the town, and in an aimless, petty kind of way anti-European feeling was very bitter.

For the random variables below, indicate whether you would expect the distribution to be best described as geometric, binomial, Poisson, exponential, uniform, or normal. For each item, give a brief explanation of your answer.

a) The number of heads in 13 tosses of a coin.

b) The number of at-bats (attempts) required for a baseball player to get his first hit.

c) The height of a randomly chosen adult female.

d) The time of day that the next major earthquake occurs in Southern California.

e) The number of automobile accidents in a town in one week.

f) The amount of time before the first score in a lacrosse game.

g) The number of times a die needs to be rolled before a 3 appears.

h) The number of particles emitted by a radioactive substance in five seconds.

For each example below, say whether the person is geographically mobile or immobile, and whether the person is occupationally mobile or immobile:

A) Christiano, a soccer player who will play for whatever team pays him the most

B) Shelly, who takes any low‐skilled job in town but doesn’t want to abandon her mother in the local nursing home

C) Adam, who maximizes his leisure time by working only 3 months per year by taking any high risk job out there

D) Diane, a very bad church organist who majored in organ who is afraid to leave her job because she probably couldn’t get hired anywhere else

E) Marta, a travel nurse

You want to write a simple python program for a food delivery company that asks the office worker how many drivers they require to deliver their packages to different parts of town. When the user enters the number of drivers, the program will ask how many packages each driver will carry to its destination. It will then calculate the total number of packages and display the result on the screen as below.

Sample run: How many drivers do you need? 5

Packages for driver 1: 3

Packages for driver 2: 4

Packages for driver 3: 1

Packages for driver 4: 12

Packages for driver 5: 8

5 drivers delivered a total of 28 packages.

note: please do not use (break) or directories

1) a) A drawer contains 9 white socks and 7 black socks. Two different socks are selected from the drawer at random. What is the probability that both of the selected socks are white?

b) A box contains 10 white marbles and 7 black marbles. Suppose we randomly draw a marble from the box, replace it, and then randomly draw another marble from the box. (This means that we might observe the same marble twice). What is the probability that both the marbles are white?

c) Suppose that 3.4 % of the items produced by a factory are defective. If 5 items are chosen at random, what is the probability that none of the items are defective?

d) Suppose that 5.7 % of the items produced by a second factory are defective. If 5 items are chosen at random from the second factory, what is the probability that exactly one of the items is defective?

2) a) Suppose that 8.8 % of the items produced by a third factory are defective. If 5 items are chosen at random from the third factory, what is the probability that exactly two of the items are defective?

b) Suppose that 5.1 % of the items produced by a fourth factory are defective. If 5 items are chosen at random from the fourth factory, what is the probability that at least two of the items are defective?

c) Suppose that 9.6 % of the items produced by a fifth factory are defective. If 6 items are chosen at random from the fifth factory, what is the expected value (or mean value) for the number of defective items?

d) In a certain town, 19 % of the population develop lung cancer. If 25 % of the population are smokers and 85% of those developing lung cancer are smokers, what is the probability that a smoker in this town will develop lung cancer?

e) . A certain kind of light bulb has a 8.5 percent probability of being defective. A store receives 54 light bulbs of this kind. What is the expected value (or mean value) of the number of light bulbs that are expected to be defective?

Question 5

Treble Inc. planned and manufactured 259,000 units of its single product in 2019, its first year of operations. Variable manufacturing costs were $48 per unit of production. Planned and actual fixed manufacturing costs were $618,000. Marketing and administrative costs (all fixed) were $309,000 in 2019. Treble Inc. sold 209,000 units of product in 2019 at $78 per unit.

Variable costing operating income for 2019 is calculated to be: (Do not round intermediate calculations. Round your final answers to whole dollar amounts.)

Multiple Choice

• $4,191,000.

• $4,400,000.

• $5,343,000.

• $5,461,490.

• $6,286,000.

Sand and Sea Resorts owns and operates two resorts in a coastal town. Both resorts are located on a barrier island that is connected to the mainland by a high bridge. One resort is located on the beach and is called the Crystal Coast Resort. The other resort is located on the inland waterway which passes between the town and the mainland; it is called the Harborview Resort. Some key information about the two resorts for the current year is shown below.

The nontraceable operating costs of the resort amount to $4,000,000. By careful study, the management accountant at Sand and Sea has determined that, while the costs are not directly traceable, the total of $4 million could be fairly allocated to the four cost drivers as follows.

Using the information regarding the allocation of the $4 million to the four cost drivers, determine the amount of cost to be allocated to the Harborview Resort.

Multiple Choice

• $1,055,000.

• $899,250.

• $1,507,000.

• $718,000.

• $1,688,000.

On the morning of March 5, 1996, a train with 14 tankers of propane derailed near the center of the small Wisconsin town of Weyauwega. Six of the tankers were ruptured and burning when the 1700 residents were ordered to evacuate the town. Researchers study disasters like this so that effective relief efforts can be designed for future disasters. About half of the households with pets did not evacuate all of their pets. A study conducted after the derailment focused on problems associated with retrieval of the pets after the evacuation and characteristics of the pet owners. One of the scales measured "commitment to adult animals," and the people who evacuated all or some of their pets were compared with those who did not evacuate any of their pets. Higher scores indicate that the pet owner is more likely to take actions that benefit the pet. Here are the data summaries.

Analyze the data and prepare a short report describing the results. (Use α = 0.01. Round your value for t to three decimal places and your P-value to four decimal places.)

State your conclusion.

Reject the null hypothesis. There is not significant evidence of a higher mean score for people who evacuated all or some pets.

Fail to reject the null hypothesis. There is significant evidence of a higher mean score for people who evacuated all or some pets.     

Fail to reject the null hypothesis. There is not significant evidence of a higher mean score for people who evacuated all or some pets.

Reject the null hypothesis. There is significant evidence of a higher mean score for people who evacuated all or some pets.

Imperfect Competition — End of Chapter Problem

Suppose that the inverse market demand for pumpkins is given by ?=$10−0.05?. Pumpkins can be grown by anybody at a constant marginal cost of $1.

a. If there are lots of pumpkin growers in town, so that the pumpkin industry is competitive, what will be the equilibrium price (P), and how many pumpkins (Q) will be sold?

P = $

Q =

b. Suppose that a freak weather event wipes out the pumpkins of all but two producers, Linus and Lucy. Both Linus and Lucy have produced bumper crops and have more than enough pumpkins available to satisfy the demand at even a zero price. If Linus and Lucy collude to generate monopoly profits, how many pumpkins will they sell, and what price will they sell for?

Q =

P = $

c. Suppose that the predominant form of competition in the pumpkin industry is price competition. In other words, suppose that Linus and Lucy are Bertrand competitors. What will be the final price of pumpkins in this market—in other words, what is the Bertrand equilibrium price? At the Bertrand equilibrium price, what will be the final quantity of pumpkins sold by both Linus and Lucy individually and for the industry as a whole?

P = $

Q_Linus =

Q_Lucy =

Q_industry =

d. In this scenario, Linus and Lucy will each earn

zero economic profits.

e. Suppose Linus lets it be known that his pumpkins are the most orange in town, and Lucy lets it be known that hers are the tastiest. The results you found in parts c and d would continue to hold to the extent that customers are

willing to substitute Linus's and Lucy's pumkins for one another.

f. Suppose Linus could grow pumpkins at a marginal cost of $0.95. What would be Linus's price and quantity? (Hint: assume Linus will price his product so as to undercut Lucy by the least amount possible.)

P_Linus = $

Q_Linus =

g. In this scenario, Lucy's output would

fall to zero.

Python

While traveling home for the holiday, you wondered how much time you'd save if you drove faster. The distance home is 120 miles, and you decided to compare driving 55 mph versus 70 mph. You also wondered if driving faster around town really saves you that much time. The around-town distance you chose was 5 miles, using speeds of 25 and 35 mph. Of course, you decided that no amount of times savings is worth the risk to yourself or others, but you still wanted to find the answer.

Create two functions to help calculate the travel time in hours, minutes and seconds and to display the results.

# Calculate travel time in minutes given the distance in miles and the speed in mph
calc_travel_time ( distance, speed )

# Output the travel time hours, minutes and seconds given distance and speed
print_travel_time ( distance, speed )

Your Python solution must include the following:

• The calc_travel_time() function will return the travel time in minutes
• The print_travel_time() function will use (call) the calc_travel_time() function, and will determine the actual time in hours, minutes and seconds, using the int() and round() Python functions
• Include the single line comment above each function
• Comment the test section of your program
• Include the standard class ''' comment section at the top of your file
• Include a section called References that lists the web site reference link

Tip:

Expected output:

To travel 120 miles at 55 MPH will take 2 hr, 10 min and 55 sec
To travel 120 miles at 70 MPH will take 1 hr, 42 min and 51 sec
To travel 5 miles at 25 MPH will take 0 hr, 12 min and 0 sec
To travel 5 miles at 35 MPH will take 0 hr, 8 min and 34 sec