1. A random sample of 10 drivers reported the below-average mileage in the city for their cars. 18, 21, 24, 25, 25, 25, 25, 26, 29, & 31. The mean of the sample is 24.9 miles per gallon, with an associated standard deviation of about 3.6. Assuming the population mean =3.71. Find the 95% confidence interval for the average mileage of the cars for all of the drivers in the class.

9) for the reaction
[ 2Al + 3H2SO4 → Al2(SO4)3 + 3 H2SO4] 6.0 g of Al (MW=26.98 g/mol) are added to 12.0 mL of 0.20 M of H2SO4

A) what is the limiting reagent in the above reaction?

b) how many miles of H2SO4 will be formed?

c) how many grams of Al2(SO4)3 (MW=342.15 g/mol) are produced in the reaction?

Homework 6: Present Value

We sought out a soothsayer, who did sayeth some sooth. She stirred her cauldron and foresaw that terrible things would happen to Evanston. 100 years from this very day, the crimes of John Evans will come back to punish the residents of this town, causing $300 million dollars of damages. However, we can avert this terrible fate at the low, low cost of just $6 million dollars today (paid to descendants of those Evans wronged). That’s right, for just $6 million dollars now, we can avert $300 million dollars of damage to future Evanston residents! You can’t beat this deal!

1. What is the most we would be willing to pay to avert this future harm if our discount rate is 1.4% per year?

2. What is the most we would be willing to pay to avert this future harm if our discount rate is 4% per year?

3. What is the most we would be willing to pay to avert this future harm if our discount rate is 10% per year?

Suppose that we could buy a bit of Evanston lakefront for $130 million and build a lovely public beach that would deliver social benefits of $5 million dollars per year forever, starting one year from now.

4. What is the most we would be willing to pay to build this park if our discount rate is 1.4% per year?

5. What is the most we would be willing to pay to build this park if our discount rate is 4% per year?

6. What is the most we would be willing to pay to build this park if our discount rate is 10% per year?

7. Think of the basic Pigouvian Externality situation.

Private Marginal Benefit = 600 - 2*Q

Private Marginal Cost = 30 + Q

Marginal Damage = 90

Private market equilibrium quantity = Q_P = (600-30)/(2+1) = 190

What is the optimal Pigouvian tax and socially optimal quantity?

8. Same setup as in the previous problem, except that the Marginal Damage doesn’t occur now, but will actually happen in 10 years. Let the discount rate be 3%.

What is the optimal Pigouvian tax and socially optimal quantity today?

9. Same setup as in the previous problem, except we just had an election, and so now the discount rate is 7%. What is the optimal Pigouvian tax now? What is the optimal social quantity today?

For Part 2 of this assignment, you will use the “Assignment 1 – Linear Kinematics Data” excel file. In the data set you are provided with vertical position and time data for a person’s vertical center of mass motion for an unspecified movement task.

You will utilize excel in all (well, some…) of its glory to calculate the vertical velocity and vertical acceleration data from the position and time data provided in the excel file. Again you will use the First Central Difference Method to calculate velocity and acceleration at each frame. Once the velocity and acceleration data have been calculated, plot the position, velocity, and acceleration data against time, either as one graph per variable or all three variables on one graph (using primary and secondary axes). Be sure to label the graphs neatly and appropriately such that you would be confident including them in a formal presentation based on the instructions provided in the tutorials.

1. Between 1 and 1.5 seconds, what direction is the person moving? Are they speeding up, slowing down, or both during this time period?
2. Between 1.75 and 2 seconds, was the acceleration positive, negative, or both? In addition, was the person moving upward, downward, or both during this time period?
3. At approximately what time is the person moving at the fastest velocity and in what direction are they moving at this time?
4. Based on your understanding of the position-velocity-acceleration relationship, what human movement does this data represent assuming the data represent the entire movement task from start to finish?

1)      Surrounding the Great Lake are four paper-mills, each producing 100 tons of paper per year. The paper is sold on the national market for $2 per ton, and including all the costs of production, costs for each firm are $1 per ton. Thus each firm earns a pure economic profit of $1 per ton. These paper mills require fresh water to operate and also produce a pollutant, which they dump into the Great Lake. New paper mills can also locate on the Great Lake, and produce at a base cost of $1 per ton. However, for each new paper mill which arrives (i.e., starting with the 5th mill), the water will become more polluted, and each firm will have to install a water treatment facility to obtain fresh water. This externality associated with new plants will raise the costs of paper production at all facilities, including the new one, by $.15 per ton for each new mill.

a. Fill in the table below to help you with your answers. which compares average revenues with average and marginal costs as new firms locate around the lake. (2 points)

b. Assume there is free access to the Great Lake. If paper mills will continue to locate as long as their is any economic profit to be earned, how many new mills will be built (i.e., the open access solution? (2 points)

c. What is the number of mills that maximizes total combined profits for the paper producers? (Hint: Average revenue remains constant at $2 (i.e, the efficient solution)?. What are these profits (resource rents) if the efficient solution? (2 points)

d. Suppose that government regulation reduced the number of mills by one from the number that would have resulted given free access. Show that the increase in profits to the remaining firms (the resource rent) is sufficient to compensate the firm that is denied access its lost profits. (2 points)

2) Suppose the state is trying to decide how many miles of a scenic river it should preserve. There are 100 people in the community, each of whom has an identical inverse demand function given by P=10-1.0q, where q is the number of miles preserved and P is the per-mile-price he or she is willing to pay for the q miles of preserved river. If the marginal cost of preservation is $500 per mile, how many miles would be preserved in an efficient allocation? (2 points)

Curly Hair is a Brazilian start-up that offers a wide portfolio of hair products (shampoo, conditioner, foam, serum…) specifically designed to take care of curly hair.

Curly Hair manufactures its products in three different plants and sells them in five markets around the country. The plants have a certain manufacturing capacity. In the tables below, you can find the demand for each market, the capacity of each plant, and the distances (in miles) between plants and markets.

The operations manager of the company proposes to redesign the transportation network and start using some distribution centers (DCs) as an intermediary step between plants and final markets. There are four DCs that could be used. These DCs have a certain capacity and they cannot be used as warehouses (they do not keep stock), products must just flow through them.

In the tables below you will find the maximum capacity of each DCs, the distances between plants and DCs, and the distances between DC and markets.

The inbound transportation cost (from plants to DCs) is 2.61 Brazilian reals per liter per mile, and the outbound transportation cost (from DCs to markets) is 3.02 Brazilian reals per liter per mile. There is also a fixed cost of 5,000 Brazilian reals for each DC that the company decides to use.

Design a distribution network that can use these DCs. What is the optimal cost (transportation + fixed cost) under this new situation?

An oil tanker has hit a sand bar and ripped a hole in the hull of the ship. Oil has begun leaking from the tanker. The oil is leaking from the ship forming a circle around it. The radius of the circle is increasing at a rate of 2.3 feet per hour. Please assist the Wild Life Federation with the following calculations. Thank you in advance for your assistance. (Round all answers to the nearest tenths place unless otherwise specified, use the π button on your calculator for calculations.) 1) A) Write the radius of the circle as a function of time. Use t as the symbol to represent time (you will need to use the information found in the news clip above.) B) What is the radius of the circle after 2 hours? C) What is the radius of the circle after 2.5 hours? D) If the oil tanker is 250 yards from shore, when will the oil first reach the shoreline? (Remember to convert to feet) 2) Write the area of the circle as a function of the radius. Use the symbol r to represent the radius. 3) A) Using the functions found in questions 1 and 2, write a function that represents area as a function of time. B) What is the area of the circle after 2 hours? C) What is the area of the circle after 2.5 hours? D) What is the area of the circle after 3 hours? E) What is the area of the circle after 3.5 hours? Math 171 Unit 1 Lab 4) Compute the average rate of change per hour for the area from 2 to 2.5 hours. 5) Compute the average rate of change per hour for the area from 3 to 3.5 hours. 6) Based upon the results found in questions 4 and 5 what is happening to the average rate of change of the area of the circle as time passes? (Increasing, Decreasing, Constant?) 7) If the tanker is 250 yards from the shore, how long will it be until 8 miles of shoreline is contaminated with oil? Round to the nearest number of days. (For the benefit of this problem, the shore is straight and if you were to draw a line perpendicular to the shore 250 yards you would find the boat, the spread will be 4 miles to either side of the ship, refer to the diagram below. Hint 1mi=5280 ft.) A) Use the figure below and find the length of the radius in feet. B) Using your formula from problem 1A, find the time in hours. C) The original question asks for the time measured in days. Convert your answer from 7B to days, rounding to the nearest number of days. Radius Radius 250 yds 4 miles 4 miles

An energy company wants to choose between two regions in a state to install​ energy-producing wind turbines. A researcher claims that the wind speed in Region A is less than the wind speed in Region B. To test the​ regions, the average wind speed is calculated for

60

days in each region. The mean wind speed in Region A is

13.7

miles per hour. Assume the population standard deviation is

2.7

miles per hour. The mean wind speed in Region B is

15.3

miles per hour. Assume the population standard deviation is

3.1

miles per hour. At

alphaαequals=0.05,

can the company support the​ researcher's claim? Complete parts​ (a) through​ (d) below.​(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

What is the​ claim?

A.

The wind speed in Region A is not greater than the wind speed in Region B.

B.

The wind speed in Region A is the same as the wind speed in Region B.

C.

The wind speed in Region A is less than the wind speed in Region B.

D.

The wind speed in Region A is not less than the wind speed in Region B.

Let Region A be sample 1 and let Region B be sample 2. Identify

Upper H 0H0

and

Upper H Subscript aHa.

Upper H 0H0​:

mu 1μ1

▼

less than<

not equals≠

greater than>

greater than or equals≥

less than or equals≤

mu 2μ2

Upper H Subscript aHa​:

mu 1μ1

▼

less than or equals≤

less than<

greater than or equals≥

greater than>

not equals≠

mu 2μ2

​(b) Find the critical​ value(s) and identify the rejection region.

The critical​ value(s) is/are

z 0z0equals=nothing.

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

What is the rejection​ region? Select the correct choice below and fill in the answer​ box(es) within your choice.

​(Round to three decimal places as​ needed.)

A.

zless than<nothing

B.

zless than<nothing

or

zgreater than>nothing

C.

zgreater than>nothing

​(c) Find the standardized test statistic z.

zequals=nothing

​(Round to two decimal places as​ needed.)

​(d) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

▼

Reject

Fail to reject

Upper H 0H0.

There

▼

is not

is

enough evidence at the

55​%

level of significance to

▼

support

reject

the​ researcher's claim that the wind speed in Region A is

▼

not greater than

less than

the same as

not less than

the wind speed in Region B.

Click to select your answer(s).

1) Golf-course designers have become concerned that old courses are becoming obsolete since new technology has given golfers the ability to hit the ball so far. Designers, therefore, have proposed that new golf courses need to be built expecting that the average golfer can hit the ball more than 255255 yards on average. Suppose a random sample of 135 golfers be chosen so that their mean driving distance is 252.5 yards. The population standard deviation is 42.6 Use a 5% significance level.

Calculate the followings for a hypothesis test where ?0:?=255: and ?1:?<255

(a)    The test statistic is    

(b)    The P-Value is

The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) ? and standard deviation ?=0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5 mg. Now, suppose a reporter wants to test whether the mean nicotine content is actually higher than advertised. He takes measurements from a SRS of 20 cigarettes of this brand. The sample yields an average of 1.45 mg of nicotine. Conduct a test using a significance level of ?=0.05

(a) The test statistic  

(b) The critical value, z* =

A random sample of 100 observations from a population with standard deviation 11.99 yielded a sample mean of 92.

1. Given that the null hypothesis is ?=90 and the alternative hypothesis is ?>90 using ?=.05α, find the following:

(a) Test statistic =
(b)  P - value:

Given that the null hypothesis is ?=90 and the alternative hypothesis is ?≠90 using ?=.05α, find the following:
(a) Test statistic ==  
(b)  P - value:

It is necessary for an automobile producer to estimate the number of miles per gallon achieved by its cars. Suppose that the sample mean for a random sample of 150 cars is 30.7 miles and assume the standard deviation is 2.1 miles. Now suppose the car producer wants to test the hypothesis that ? the mean number of miles per gallon, is 28 against the alternative hypothesis that it is not 28. Conduct a test using ?=.05 by giving the following:

(a)    positive critical ? score    

(b)    negative critical ? score    

(c)    test statistic

35 people are randomly selected and the accuracy of their wristwatches is checked, with positive errors representing watches that are ahead of the correct time and negative errors representing watches that are behind the correct time. The 35 values have a mean of 107sec and a standard deviation of 218sec. Use a 0.01significance level to test the claim that the population of all watches has a mean of 0 sec.

The test statistic is

The P-Value is

Given the significance level ?=0.07 find the following:

(a)    left-tailed ?z value
?=

(b)    right-tailed z value
?=

(c)    two-tailed ? value
|?|=

QUESTION 1

1. Computers in some vehicles calculate various quantities related to car performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas tank was filled, and the computer was then reset. In addition to the computer-calculated mpg, the driver also recorded the miles per gallon by dividing the miles driven by the number of gallons at each fill-up.

   The data for a random sample of 20 of these the mpg values given in the csv file under variables Computer, Driver and Difference = (Computer – Driver).

   (Q1-9)Question: You suspect that that the car on-board-computer has been over-estimating the 41-mpg stated at the car-manufacturing website.

   Download the data file, Ch5_FuelEfficiency.csv, from Blackboard, and get the basic descriptive statistics for all three variables: Computer, Driver and Difference, using the following R codes:

   mydata <- read.csv("Ch5_FuelEfficiency.csv")

   #install.packages("pastecs")

   library(pastecs)

   stat.desc(mydata)

   The mean values for variables Computer, Driver and Differrence are 43.17, 40.44 and 2.73, respectively.

   Part I: Statistical inference for variable “Computer”

   1. Implement the hypothesis testing.

   a. State the hypotheses.

   Question 1: choose the right hypotheses for this problem.

   		H0: = =41   vs.    Ha: > 41
   		H0: = =41   vs.    Ha: ><41
   		H0: = =41   vs.    Ha:   ≠ 41
   		H0: = =43.17   vs.    Ha:   >43.17

2. QUESTION 2

3. b. Perform the test of significance using α = 5% and state/interpret your conclusion.

   Known:  n = 20, = 43.17 (Statistic), s = 4.41 (we use this as an estimate for σ)

   Question 2: What is the standard error?_________

   		4.41
   		3.5
   		3
   		0.9861